Circles CPP#01,02,03 PDF
Circles CPP#01,02,03 PDF
Circles CPP#01,02,03 PDF
CPP# 01
Question
based on Standard forms of Equation of a Circle
Q.9 The coordinates of any point on the circle
x2 + y2 = 4 are-
Q.1 The length of the diameter of the circle (A) (cos, sin) (B) (4cos, 4 sin)
x2 + y2 – 4x – 6y + 4 = 0 is -
(C) (2cos, 2sin) (D) (sin, cos)
(A) 9 (B) 3 (C) 4 (D) 6
Q.10 The parametric coordinates of any point on
the circle x2 + y2 – 4x – 4y = 0 are-
Q.2 Which of the following is the equation of a
(A) (– 2 + 2cos, – 2 + 2 sin)
circle?
(B) (2 + 2cos, 2 + 2 sin)
(A) x2 + 2y2 – x + 6 = 0
(B) x2 – y2 + x + y + 1 = 0 (C) (2 + 2 2 cos, 2 + 2 2 sin)
(C) x2 + y2 + xy + 1 = 0 (D) None of these
(D) 3(x2 + y2) + 5x + 1 = 0 Q.11 The parametric coordinates of a point on the
circle x2 + y2 – 2x + 2y – 2 = 0 are -
Q.3 The equation of the circle passing through (A) (1 – 2 cos , 1 – 2 sin )
(3, 6) and whose centre is (2, –1) is - (B) (1+ 2 cos , 1 + 2 sin )
(A) x2 + y2 – 4x + 2y = 45 (C) (1+ 2 cos , – 1 + 2 sin )
(B) x2 + y2 – 4x – 2y + 45 = 0 (D) (–1 + 2 cos , 1 + 2 sin )
(C) x2 + y2 + 4x – 2y = 45
(D) x2 + y2 – 4x + 2y + 45 = 0 Q.12 The equation k (x2 + y2) – x – y + k = 0
represents a real circle, if-
Q.4 If (4, 3) and (–12, –1) are end points of a (A) k < 2 (B) k > 2
diameter of a circle, then the equation of the 1
circle is- (C) k > 1/ 2 (D) 0 < |k|
2
(A) x2 + y2 – 8x – 2y – 51 = 0
Q.13 If the equation
(B) x2 + y2 + 8x – 2y – 51 = 0
px2 + (2–q)xy + 3y2 – 6qx + 30 y + 6q = 0
(C) x2 + y2 + 8x + 2y – 51 = 0 represents a circle, then the values of p and q
(D) None of these are -
(A) 2, 2 (B) 3, 1 (C) 3, 2 (D) 3, 4
Q.5 The radius of the circle passing through the
points (0, 0), (1, 0) and (0, 1) is- Q.14 The circle represented by the equation
(A) 2 (B) 1/ 2 (C) 2 (D) 1/2 x2 + y2 + 2gx + 2fy + c = 0 will be a point circle,
if-
Q.6 The radius of a circle with centre (a, b) and (A) g2 + f 2 = c (B) g2 + f 2 + c = 0
passing through the centre of the circle (C) g2 + f 2 > c (D) None of these
x2 + y2 – 2gx + f 2 = 0 is-
Q.15 The equation of the circum-circle of the triangle
(A) (a g ) 2 b 2 (B) a 2 (b g) 2
x y
formed by the lines x = 0, y = 0, – = 1, is -
(C) a 2 (b g ) 2 (D) (a g ) 2 b 2 a b
Q.7 If (x, 3) and (3, 5) are the extremities of a (A) x2 + y2 + ax – by = 0
diameter of a circle with centre at (2, y). Then (B) x2 + y2 – ax + by = 0
the value of x and y are- (C) x2 + y2 – ax – by = 0
(A) x = 1, y = 4 (B) x = 4, y = 1 (D) x2 + y2 + ax + by = 0
(C) x = 8, y = 2 (D) None of these
Q.8 If (0, 1) and (1, 1) are end points of a diameter Q.16 The circum-circle of the quadrilateral formed by
of a circle, then its equation is- the lines x = a, x = 2a, y = – a, y = a is-
(A) x2 + y2 –x –2y + 1 = 0 (A) x2 + y2 – 3ax – a2 = 0
(B) x2 + y2 + x –2y + 1 = 0 (B) x2 + y2 + 3ax + a2 = 0
(C) x2 + y2 –x –2y – 1 = 0 (C) x2 + y2 – 3ax + a2 = 0
(D) None of these (D) x2 + y2 + 3ax – a2 = 0
Q.17 The x coordinates of two points A and B are roots Q.24 The point where the line x = 0 touches the circle
of equation x2 + 2x – a2 = 0 and y coordinate are x2+ y2 – 2x – 6y + 9 = 0 is-
roots of equation y2 + 4y – b2 = 0 then equation (A) (0, 1) (B) (0, 2)
of the circle which has diameter AB is- (C) (0, 3) (D) No where
(A) (x – 1)2 + (y – 2)2 = 5 + a2 + b2
Q.25 Circle x2 + y2 + 6y = 0 touches -
(B) (x + 1)2 + (y + 2)2 = (5 a 2 b 2 )
(A) x– axis at the point (3, 0)
(C) (x + 1)2 + (y + 2)2 = (a2 + b2) (B) x– axis at the origin
(D) (x + 1)2 + (y + 2)2 = 5 + a2 + b2 (C) y – axis at the origin
(D) The line y + 3 = 0
Question
based on Equation of Circle in special cases
Question
based on Position of Point w.r.t. Circle
Q.18 A circle touches both the axes and its centre
lies in the fourth quadrant. If its radius is Q.26 Position of the point (1, 1) with respect to the
1 then its equation will be - circle x2 + y2 – x + y – 1 = 0 is -
(A) x2 + y2 – 2x + 2y + 1 = 0 (A) Outside the circle (B) Inside the circle
(B) x2 + y2 + 2x – 2y – 1 = 0 (C) Upon the circle (D) None of these
(C) x2 + y2 – 2x – 2y + 1 = 0
(D) x2 + y2 + 2x – 2y + 1 = 0 Q.27 The point (0.1, 3.1) with respect to the circle
x2 +y2 – 2x – 4y + 3 = 0, is -
Q.19 The equation to a circle with centre (2, 1) (A) Inside the circle but not at the centre
and touching x axis is - (B) At the centre of the circle
(A) x2 + y2 + 4x + 2y + 4 = 0 (C) On the circle
(B) x2 + y2 – 4x – 2y + 4 = 0 (D) Outside the circle
(C) x2 + y2 – 4x – 2y + 1 = 0
Question
(D) None of these based on Line & Circle
Q.20 The equation to the circle whose radius is
4 and which touches the x–axis at a distance Q.28 The straight line (x – 2) + (y + 3) = 0 cuts the
–3 from the origin is- circle (x –2)2 + (y –3)2 = 11 at-
(A) x2 + y2 – 6x + 8y – 9 = 0 (A) no points (B) two points
(B) x2 + y2 ± 6x – 8y + 9 = 0 (C) one point (D) None of these
(C) x2 + y2 + 6x ± 8y + 9 = 0
(D) x2 + y2 ± 6x – 8y – 9 = 0 Q.29 If the line 3x + 4y = m touches the circle
x2 + y2 = 10x, then m is equal to-
Q.21 The equation of the circle touching the lines (A) 40, 10 (B) 40, –10
x = 0, y = 0 and x = 2c is- (C) –40, 10 (D) –40, –10
(A) x2 + y2 + 2cx + 2cy + c2 = 0
(B) x2 + y2 – 2cx + 2cy + c2 = 0 Q.30 Circle x2 + y2 – 4x – 8y – 5 = 0 will intersect the
(C) x2 + y2 ± 2cx – 2cy + c2 = 0 line 3x – 4y = m in two distinct points, if -
(D) x2 + y2 – 2cx ± 2cy + c2 = 0 (A) –10 < m < 5 (B) 9 < m < 20
(C) –35 < m <15 (D) None of these
Q.22 The circle x2 + y2 – 4x – 4y + 4 = 0 is-
(A) touches x–axes only Q.31 The length of the intercept made by the circle
(B) touches both axes x2 + y2 =1 on the line x + y = 1 is-
(C) passes through the origin (A) 1/ 2 (B) 2
(D) touches y–axes only
(C) 2 (D) 2 2
Q.23 If a be the radius of a circle which touches
x-axis at the origin, then its equation is- Q.32 If a circle with centre (0, 0) touches the line
(A) x2 + y2 + ax = 0 5x + 12y = 1 then its equation will be-
(B) x2 + y2 ± 2ya = 0 (A) 13(x2 + y2) = 1 (B) x2 + y2 = 169
(C) x2 + y2 ± 2xa = 0 (C) 169(x2 + y2) = 1 (D) x2 + y2 = 13
(D) x2 + y2 + ya = 0
Q.33 The equation of circle which touches the Q.41 The gradient of the tangent line at the point
x y (a cos , a sin ) to the circle x2 + y2 = a2, is-
axes of coordinates and the line + = 1 and
3 4 (A) tan ( – ) (B) tan
whose centre lies in the first quadrant is (C) cot (D) – cot
x2 + y2 – 2cx – 2cy + c2 = 0, where c is-
(A) 2 (B) 0 Q.42 If y = c is a tangent to the circle
(C) 3 (D) 6 x2 + y2 – 2x + 2y –2 = 0 at (1, 1), then the value
of c is-
Q.34 For the circle x2 + y2 – 2x + 4y – 4 = 0, the line (A) 1 (B) 2
2x – y + 1 = 0 is a- (C) –1 (D) – 2
(A) chord (B) diameter
(C) tangent line (D) None of these Q.43 Line 3x + 4y = 25 touches the circle x2 + y2 = 25
at the point-
Q.35 The line y = x + c will intersect the circle (A) (4, 3) (B) (3, 4)
x2 + y2 = 1 in two coincident points, if- (C) (–3,–4) (D) None of these
(A) c = – 2 (B) c = 2
Q.44 The equations of the tangents drawn from the
(C) c = ± 2 (D) None of these
point (0, 1) to the circle x2 + y2 – 2x + 4y = 0 are-
Q.36 Centre of a circle is (2, 3). If the line (A) 2x – y + 1 = 0, x + 2y – 2 = 0
x + y = 1 touches it. Find the equation of circle- (B) 2x – y – 1 = 0, x + 2y – 2 = 0
(A) x2 + y2 – 4x – 6y + 5 = 0 (C) 2x – y + 1 = 0, x + 2y + 2 = 0
(B) x2 + y2 – 4x – 6y – 4 = 0 (D) 2x – y – 1 = 0, x + 2y + 2 = 0
(C) x2 + y2 – 4x – 6y – 5 = 0
(D) None of these Q.45 The tangent lines to the circle x2 + y2 – 6x + 4y =12
which are parallel to the line 4x + 3y + 5 = 0 are
Q.37 The lines 12 x – 5y – 17 = 0 and 24 x – 10 y + 44 =0 given by-
are tangents to the same circle. Then the radius (A) 4x + 3y – 7 = 0, 4x + 3y + 15 = 0
of the circle is- (B) 4x + 3y – 31 = 0, 4x + 3y + 19 = 0
1 (C) 4x + 3y – 17 = 0, 4x + 3y + 13 = 0
(A) 1 (B) 1
2 (D) None of these
(C) 2 (D) None of these
Q.46 The equations of tangents to the circle
Q.38 If the circle x2 + y2
= a2
cuts off a chord of x2 + y2 – 22x – 4y + 25 = 0 which are
length 2b from the line y = mx + c, then- perpendicular to the line 5x + 12y + 8 = 0 are-
(A) (1–m2) (a2 – b2) = c2 (A) 12x – 5y + 8 = 0, 12x – 5y = 252
(B) (1+ m2) (a2 – b2) = c2 (B) 12x – 5y – 8 = 0, 12x – 5y + 252 = 0
(C) (1–m2) (a2 + b2) = c2
(C) 12x – 5y = 0, 12x – 5y = 252
(D) None of these
(D) None of these
Question
Equation of Tangent & Normal Q.47 The equation of the normal to the circle
based on
1 1
x2 + y2 = 9 at the point , is-
Q.39 x + my + n = 0 is a tangent line to the circle 2 2
x2 + y2 = r2, if-
2
(A) 2 + m2 = n2 r2 (B) 2 + m2 = n2 + r2 (A) x – y = (B) x + y = 0
3
(C) n2 = r2 (2 + m2) (D) None of these (C) x – y = 0 (D) None of these
Q.48 The equation of the normal at the point (4, –1)
Q.40 The equation of the tangent to the circle
of the circle x2 + y2 – 40x + 10y = 153 is-
x2 + y2 = 25 which is inclined at 60º angle with
(A) x + 4y = 0
x-axis, will be-
(B) 4x + y = 3
(A) y = 3 x ± 10 (B) y = 3 x ± 2 (C) x – 4y = 0
(C) 3 y = x ± 10 (D) None of these (D) 4x – y = 0
Q.49 The equation of the normal to the circle Q.58 The angle between the tangents drawn from the
x2 + y2 – 8x – 2y + 12 = 0 at the points whose origin to the circle (x–7)2 + (y + 1)2 = 25 is-
ordinate is – 1, will be- (A) /3 (B) /6
(A) 2x – y – 7 = 0, 2x + y – 9 = 0 (C) /2 (D) /8
(B) 2x + y – 7 = 0, 2x + y + 9 = 0
(C) 2x + y + 7 = 0, 2x + y + 9 = 0 Question
(D) 2x – y + 7 = 0, 2x – y + 9 = 0 based on Chord of Contact
Q.50 The line ax + by + c = 0 is a normal to the circle Q.59 The equation of the chord of contact of the
x2 + y2 = r2. The portion of the line ax+ by + c = 0 circle x2 + y2 + 4x + 6y – 12 = 0 with respect
intercepted by this circle is of length- to the point (2, –3) is-
(A) r2 (B) r (A) 4x = 17 (B) 4x + y = 17
(C) 4y = 17 (D) None of these
(C) 2 r (D) r
Q.60 The equation of the chord of contact, if the
Question tangents are drawn from the point (5, –3) to the
based on Length of Tangent & Pair of Tangents
circle x2 +y2 = 10, is-
Q.51 If the length of tangent drawn from the point (A) 5x – 3y = 10 (B) 3x+ 5y = 10
(5,3) to the circle x2 + y2 + 2x + ky + 17 = 0 is (C) 5x + 3y = 10 (D) 3x –5y = 10
7, then k =
(A) – 6 (B) – 4 (C) 4 (D) 13/2 Question
based on Director Circle
Q.52 The length of tangent from the point (5, 1) to Q.61 The equation of director circle to the circle
the circle x2 + y2 + 6x – 4y – 3 = 0, is- x2 + y2 = 8 is-
(A) 29 (B) 81 (C) 7 (D) 21 (A) x2 + y2 = 8 (B) x2 + y2 =16
(C) x2 + y2 = 4 (D) x2 + y2 = 12
Q.53 The length of the tangent drawn from the point
(2, 3) to the circle 2(x2 + y2) – 7x + 9y – 11 = 0 Q.62 Two perpendicular tangents to the circle
x2 + y2 = a2 meet at P. Then the locus of P has
(A) 18 (B) 14 (C) 14 (D) 28 the equation-
(A) x2 + y2 = 2a2 (B) x2 + y2 = 3a2
Q.54 If the lengths of the tangents drawn from the 2 2
(C) x = y = 4a 2 (D) None of these
point (1, 2) to the circles x2 + y2 + x + y – 4 = 0
and 3x2 + 3y2 –x –y+k =0 be in the ratio 4 : 3, Question
then k = based on Position of Two Circle
(A) 21/2 (B) 7/2 (C)–21/4 (D) 7/4
Q.63 Consider the circle x2 + (y – 1)2 = 9,
Q.55 A pair of tangents are drawn from the origin to (x – 1)2 + y2 = 25. They are such that-
the circle x2 + y2 + 20(x + y) + 20 = 0. (A) each of these circles lies outside the other
The equation of the pair of tangents is- (B) one of these circles lies entirely inside the
(A) x2 + y2 + 5 xy = 0 (B) x2 + y2 + 10xy = 0 other
(C) 2x2 + 2y2 + 5xy = 0 (D) 2x2 + 2y2 – 5xy = 0 (C) these circles touch each other
(D) they intersect in two points
Q.56 If the equation of one tangent to the circle with
centre at (2, –1) from the origin is 3x + y = 0, Q.64 Circles x2 + y2 – 2x – 4y = 0 and
then the equation of the other tangent through x2 + y2 – 8y – 4 = 0
the origin is- (A) touch each other internally
(A) x + 3y = 0 (B) 3x – y = 0 (B) cuts each other at two points
(C) x – 3y = 0 (D) x + 2y = 0 (C) touch each other externally
(D) None of these
Q.57 The equation of the pair of tangents drawn to the
circle x2 + y2 – 2x + 4y + 3 = 0 from (6, –5) is- Q.65 The number of common tangents of the circle
(A) 7x2 + 23y2 + 30xy + 66x + 50y – 73 = 0 x2 + y2 – 2x – 1 = 0 and x2 + y2 – 2y – 7 = 0 is-
(B) 7x2 + 23y2 – 30xy – 66x – 50y + 73 = 0 (A) 1 (B) 3
(C) 7x2 + 23y2 + 30xy – 66x – 50y – 73 = 0 (C) 2 (D) 4
(D) None of these
Q.66 If the circles x2 + y2 + 2x – 8y + 8 = 0 and Q.74 The equation of circle passing through the
x2 + y2 + 10 x – 2y + 22 = 0 touch each other, points of intersection of circles x2 + y2 = 6 and
their point of contact is- x2 + y2 – 6x + 8 = 0 and the point (1, 1) is-
17 11 11 (A) x2 + y2 – 4y + 2 = 0
(A) , (B) ,2 (B) x2 + y2 – 3x + 1 = 0
5 5 3
(C) x2 + y2 – 6x + 4 = 0
17 11 11 (D) None of these
(C) , (D) ,2
5 5 3 Q.75 The equation of the circle whose diameter is the
common chord of the circles x2 + y2 + 3x +2y + 1 = 0
Q.67 For the given circles x2 +y2 – 6x – 2y + 1 = 0
and x2 + y2 + 3x + 4y + 2 = 0 is-
and x2 + y2 + 2x – 8y+ 13 = 0, which of the
(A) x2 + y2 + 3x + y + 5 = 0
following is true-
(A) One circle lies completely outside the other (B) x2 + y2 + x + 3y + 7 = 0
(B) One circle lies inside the other (C) x2 + y2 + 2x +3 y + 1 = 0
(C) Two circle intersect in two points (D) 2 (x2 + y2) + 6x + 2y + 1 = 0
(D) They touch each other
Question
based on Common chord of two Circles
Q.68 If circles x2 + y2 = r2 and x2 + y2 – 20x + 36 = 0
intersect at real and different points, then-
Q.76 The common chord of x2+ y2 – 4x – 4y = 0 and
(A) r < 2 and r > 18 (B) 2 < r < 18
x2 + y2 = 16 subtends at the origin an angle
(C) r = 2 and r = 18 (D) None of these equal to-
Q.69 The number of common tangents that can be (A) /6 (B) /4 (C) /3 (D) /2
drawn to the circles x2 + y2 – 4x – 6y – 3 = 0
and x2 + y2 + 2x + 2y + 1 = 0 is- Q.77 The distance from the centre of the circle
(A) 1 (B) 2 (C) 3 (D) 4 x2 + y2 = 2x to the straight line passing through
the points of intersection of the two circles
Question Equation of a chord whose middle x2+ y2 + 5x – 8y + 1 = 0, x2 + y2 – 3x + 7y – 25 = 0 is-
based on point is given (A) 1 (B) 2
(C) 3 (D) None of these
Q.70 Find the locus of mid point of chords of circle
x2 + y2 = 25 which subtends right angle at origin- Q.78 The length of the common chord of the
(A) x2 + y2 = 25/4 (B) x2 + y2 = 5 circle x2 + y2 + 4x + 6y + 4 = 0 and
2 2
(C) x + y = 25/2 (D) x2 + y2 = 5/2 x2 + y2 + 6x + 4y + 4 = 0 is-
(A) 10 (B) 22 (C) 34 (D) 38
Q.71 The equation to the chord of the circle
x2 + y2 = 16 which is bisected at (2, – 1) is-
Q.79 The length of the common chord of circle
(A) 2x + y = 16 (B) 2x – y = 16
x2 + y2 – 6x – 16 = 0 and x2 + y2 – 8y – 9 = 0 is-
(C) x + 2y = 5 (D) 2x – y = 5
(A) 10 3 (B) 5 3
Q.72 The equation of the chord of the circle
(C) 5 3 /2 (D) None of these
x2 + y2 – 6x + 8y = 0 which is bisected at the
point (5, –3) is- Q.80 Length of the common chord of the
(A) 2x – y + 7 = 0 (B) 2x + y – 7 = 0 circles x2 + y2 + 5x + 7y + 9 = 0 and
(C) 2x + y + 7 = 0 (D) 2x – y – 7 = 0 x2 + y2 + 7x + 5y + 9 = 0 is-
(A) 8 (B) 9 (C) 7 (D) 6
Question
based on Circle through the Point of Intersection
Question
Q.73 The equation of the circle passing through based on Angle of intersection of two Circles
the point (1, 1) and through the point of Q.81 Two given circles x2 + y2 + ax + by + c = 0 and
intersection of circles x2 + y2 + 13x – 3y = 0 and x2 + y2 + dx + ey + f = 0 will intersect each
2x2 + 2y2 + 4x – 7y – 25 = 0 is- other orthogonally, only when-
(A) 4x2 + 4y2 – 17x – 10y + 25 = 0 (A) ad + be = c + f
(B) 4x2 + 4y2 + 30x – 13y – 25 = 0 (B) a + b + c = d + e + f
(C) 4x2 + 4y2 – 30x – 10y – 25 = 0 (C) ad + be = 2c + 2f
(D) None of these (D) 2ad + 2be = c + f
Q.82 If the circles of same radius a and centres at
(2, 3) and (5, 6) cut orthogonally, then a is equal
to-
(A) 6 (B) 4 (C) 3 (D) 10
Q.6 A circle is inscribed in an equilateral triangle of Q.12 The angle between tangents drawn from a point
side 6. Find the area of any square inscribed in P to the circle x2 + y2 + 4x – 2y – 4 = 0 is 60°.
the circle - Then locus of P is -
(A) 36 (B) 12 (C) 6 (D) 9 (A) x2 + y2 + 4x – 2y – 31 = 0
(B) x2 + y2 + 4x – 2y – 21 = 0
Q.7 The tangent at any point to the circle (C) x2 + y2 + 4x – 2y – 11 = 0
x2 + y2 = r2 meets the coordinate axes at A and (D) x2 + y2 + 4x – 2y = 0
B. If lines drawn parallel to the coordinate axes
through A and B intersect at P, the locus of P is
(A) x2 + y2 = r–2 (B) x–2 + y–2 = r2 Q.13 A circle with centre A and radius 7 is tangent to
the sides of an angle of 60°. A larger circle with
1 1 1 1 1 1 centre B is tangent to the sides of the angle and
(C) (D)
x2 y2 r2 x2 y2 r2 to the first circle. The radius of the larger circle
is
Q.18 Statement (1): If two circles
x2 + y2 + 2gx +2fy = 0 and x2 + y2 + 2g'x +2f 'y = 0
touch each other then f 'g = fg'.
•B Statement (2) : Two circle touch each other, if
•A line joining their centres is perpendicular to all
possible common tangents.
(A) 30 3 (B) 21
(C) 20 3 (D) 30 Q.19 Statement (1): If a circle passes through points
Assertion-Reason Type Question of intersection of co-ordinate axes with the lines
x – y + 1 = 0 and x – 2y + 3 = 0 then value of
The following questions (Q. 14 to 24) given
below consist of an "Assertion" (1) and is 2.
"Reason "(2) Type questions. Use the
following key to choose the appropriate Statement (2): If lines a1 x + b1y + c1 = 0 and
answer. a2x + b2y + c2 = 0 intersects. Coordinate axes at
(A) Both (1) and (2) are true and (2) is the
correct explanation of (1) a1 b1
concyclic points then .
(B) Both (1) and (2) are true but (2) is not a 2 b2
the correct explanation of (1)
(C) (1) is true but (2) is false
(D) (1) is false but (2) is true Q.20 Statement (1): Equation of circle passing
Q. 14 Statement (1): Two points A(10, 0) and through two points (2, 0) and (0, 2) and having
O(0, 0) are given and a circle x2 + y2– 6x + 8y – 11= 0. least area is x2 + y2 – 2x –2y = 0.
The circle always cuts the line segments OA.
Statement (2) : The centre of the circle, point A Statement (2): The circle of smallest radius
and the point O are not collinear. passing through two given points A and B must
Q.15 Statement (1) : If a line L = 0 is a tangents to the AB
be of radius .
circle S = 0 then it will also be a tangent to the circle 2
S + L = 0.
Statement (2) : If a line touches a circles then Q.21 Tangents are drawn from the point (2, 3) to the
perpendicular distance from centre of the circle circle x2 + y2 = 9, then
on the line must be equal to the radius. Statement (1): Tangents are mutually
perpendicular.
Q.16 Consider the following statements:-
Statement (2): Locus of point of intersection
Statement (1): The circle x2 + y2 = 1 has of perpendicular tangents is x2 + y2 = 18.
exactly two tangents parallel to the x-axis
dy Q.22 Let '' is the angle of intersection of two circles
Statement (2): = 0 on the circle exactly at
dx with centres C1 and C2 and radius r1 and r2
the point (0, ±1). respectively then.
Q.17 Statement (1): The equation of chord of the Statement (1): If cos = ±1 then, the circles
touch each other.
circle x2 + y2 – 6x + 10y – 9 = 0, which is
bisected at (–2, 4) must be x + y – 2= 0. Statement (2): Two circles touch each other if
|C1C2| = |r1 ± r2|
Statement (2) : In notations the equation of the
chord of the circle S = 0 bisected at (x1,y1) must
be T = S1.
Q.23 Statement (1): The locus of mid point of chords Q.28 Equation of circle passing through A and B
2 2 2
of circle x + y = a which are making right whose AB is diameter-
(A) x2 + y2 – 3x – 3y – 5 = 0
a2
angle at centre is x2 + y2 = . (B) x2 + y2 – 3x – 3y – 4 = 0
2
(C) x2 + y2 + 3x + 3y – 4 = 0
Statement (2): The locus of mid point of chords (D) x2 + y2 + 3x + 3y – 5 = 0
of circle x2 + y2 – 2x = 0 which passes through
origin is x2 + y2 – x = 0. Q.29 Mid point of AB is-
Passage-1 5 1 3 3
(A) , (B) ,
2 2 2 2
Passage I (Question 24 to 26) (C) (2, 1) (D) (1, 2)
Let C1, C2 are two circles each of radius 1
touching internally the sides of triangles POA1, Passage-III (Question 30 to 32)
PA1A2 respectively where P (0, 4) O is origin,
A1, A2 are the points on positive x-axis. To the circle x2 + y2 = 4 two tangents are drawn
from P(–4, 0), which touches the circle at A and
On the basis of above passage, answer the B and a rhombus PA PB is completed.
following questions:
On the basis of above passage, answer the
Q.24 Angle subtended by circle C1 at P is- following questions :
2 2
(A) tan–1 (B) 2 tan–1 Q. 30 Circumcentre of the triangle PAB is at
3 3
(A) (–2, 0) (B) (2, 0)
3 3
(C) tan–1 (D) 2 tan–1 3
4 4 (C) , 0 (D) None of these
2
Q.25 Centre of circle C2 is-
Q.31 Ratio of the area of triangle PAP to that of
1
(A) (3, 1) (B) (3 , 1) PAB is
2
(A) 2 : 1 (B) 1 : 2
3
(C) (3 , 1) (D) None of these (C) 3:2 (D) None of these
4
CPP# 02
Qus. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. B A A D A B B A A B C C A A C B B D A C
Qus. 21 22 23 24 25 26 27 28 29
Ans. B B D A D D B B C
CPP# 03
Qus. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. C D A C A C C A B A B A B B B A D C C A
Qus. 21 22 23 24 25 26 27 28 29 30 31 32
Ans. D A B C B B C B B A D A