ANALYTIC GEOMETRY

Direction: Encircle the letter of your choice.

1. A line has equation y = 4x + 5. Which of the following points lies on the line?
a. (-1, 1) b. (5, 25) c. (3, 7) d. (6, 9)

2. What is the equation of a circle with center at (-5, 7) and diameter that is 20 cm.
a. (x – 5)2 + (y + 7)2 = 100 c. (x – 5)2 + (y - 7)2 = 100
2 2
b. (x + 5) + (y + 7) = 100 d. (x + 5)2 + (y - 7)2 = 100

3. The midpoint of AB is (5, 8). Point B has coordinate of (-2, -6). What is the equation of AB?
a. y + 8 = 2 (x + 5) c. y + 6 = 1/2 (x + 2)
b. y + 6 = 2 (x + 2) d. y - 8 = 2/3 (2x - 5)

4. Find the gradient of the lines of the following pairs of point: (3, 4) and (5, -1).
3 3 4 3
a. b. c.  -5/2 d. 
8 4 5 4

5. Find the distance between points ( -3, 2 ) and ( 1, 2 ).

a. 5 b. 3 c. 9 d. 4

6. A line has equation y = 4x + 5. Which of the following points doesn’t lie on the line?
a. ( 5, 25 ) b. ( 6, 9 ) c. (-1 , 1 ) d. ( -3 , -7 )

7. The x and y – intercept of the line whose equation is 4x – 3y – 12 = 0 are.

a. ( 4, 3 ) b. ( -3 , -4 ) c. ( -3 , 12 ) d. ( 3, -12 )

8. A line passing through ( 4, -5 ) and ( -3 , 2 ). The equation of this line is:

a. x – 3y – 3 = 0 b. 4x – 2y – 5 = 0 c. x + y + 1 = 0 d. -3x – 5y + 2 = 0

9. Find the equation of the following x and y – intercept are ( 2 , -3 ) respectively.

a. 2x – 3y = 6 b. 3x + 2y = 6 c. 3x – 2y = 6 d. 2x + 3y = 6

10. Two lines perpendicular to the same plane are ___________ to each other.
a. Oblique b. Perpendicular c. Intersecting d. Parallel

11. Find the gradient of the tangent line to the curve y = x 2 and x = 1.
1
a. 1 b. -1 c. d. 2
2

12. Find the midpoint of the line segment whose two points are ( -5 , 4 ) and ( -3 , 10 ).
a. ( -4 , 8 ) b. ( -1 , 7 ) c. ( -4 , 7 ) d. ( -4 , 8 )

13. Which of the following equation passes through the origin?

a. x = y b. 3x = 4y c. x + y = 0 d. All of the above

14. What is the slope of the line that passes through ( 5 , 1 ) and ( 9 , 7 )?
1 1 1 3
a. b. c. d.
2 4 3 2

15. Find the equation of the line containing the point ( 5 , 2 ) and has a slope of -1.
a. y = 7 – x b. y = x – 7 c. y = -x – 7 d. y = 7 + x

16. Find the equation of the line passing through the point ( 0 , 2 ) and is perpendicular to the line 3x + y = 7.
a. y = -3x + 2 b. x – 3y – 6 = 0 c. 3x + y = 2 d. x – 3y + 6 = 0

MAJORSHIP IN MATH
MR. BRYAN J. MADERSE, LPT, MAEd
WVSU
 17. The center of a circle x 2  y 2  6 x  2 y  6  0 is at point.
a. ( 3 , 1 ) b. ( -1 , 3 ) c. ( -1 , - 3 ) d. ( 1 , 3 )
18. Which among the equation is the line passing through the points ( 6 , -5 ) and parallel to the line x + 6y –
10 = 0.
a. x + 6y – 36 = 0
19. The curve whose equation y 2  x 2  16  0 is symmetrical with respect to.
a. y – axis b. both x and y – axis c. y – axis d. none of these

20. In what quadrant would a point lie if its abscissa and ordinate are numerically equal but opposite in signs?
a. I and II b. I and III c. II and IV d. II and III

21. What is the area of the triangle with vertices at ( 1 , 1 ), ( 5 , 7 ) and ( 5 , 1 ).

a. 8 sq. units b. 12 sq. units c. 16 sq. units d. 10 sq. units

22. The equation of the parabola with vertex at the origin which opens to the left and passes through the
point ( -4 , 4 ) has the equation.
a. x 2  4 y b. x 2  4 y c. y 2  4 x d. y 2  4 x

23. The equation x 2  2 y  2 x  1  0 represents.

a. Point b. circle c. parabola d. ellipse

24. What is the equation of a circle with the center ( -5 , 7 ) and a radius of 10 cm?
a. ( x  5) 2  ( y  7) 2  100 c. ( x  5) 2  ( y  7) 2  100
b. ( x  5)2  ( y  7) 2  100 d. ( x  5)2  ( y  7) 2  100

25. Find the reflectional symmetry of the function ( x  3) 2   y  2 .

a. y = 2 b. x = 3 c. x = -3 d. y = -2

26. The equation that is equivalent to y 2  10 y  4 x  21  0 is.

a. ( y  5)2  4( x  1) c. ( y  5) 2  2(2 x  1)
b. ( y  4)2  4( x  3) d. ( y  2)2  2(2 x  1)

27. Find the value of k so that the graph of y  ( x  3) 2  k passes trough ( 1 , 4 ).

a. -3 b. 1 c. 3 d. 0

28. Find the equation of the line having a gradient of -1 and y-intercept of 4.
1
a. y = 2x + 4 b. y = - x+4 c. y = -x + 4 d. y = x – 4
4

29. The distance from point ( 2, 1 ) to the line 4 x  3 y  5  0 is __________ units.

a. 3 b. 2 c. 5 d. 4

30. The vertex of a parabola x 2  4 y  8  0 is at point ________.

a. ( -8, -2 ) b. ( 4 , 6 ) c. ( -4 , -6 ) d. ( 0 , -2 )

31. Find the center of a circle having the equation x 2  y 2  4 x  6 y  3 .

a. ( -2 , -3 ) b. ( 4 , 6 ) c. ( 2, -3 ) d. ( -4 , -6 )

32. Change the polar coordinates y  6 x  7.

a. r= 6 sin θ + 7 c. r = cos θ + 7
sin   6cos
b. r= 7 ( sin θ – 6 cos θ) d. r 
7

MAJORSHIP IN MATH
MR. BRYAN J. MADERSE, LPT, MAEd
WVSU
 33. Change to Cartesian equation r = a sin θ.
a. x 2  ay  y 2 b. x 2  ax  a c. x 2  y  a 2 d. ax3  y 2  a
34. Find the equation of the tangent y  x 2  6 x  4 at ( 4 , - 4).
a. x  2 y  4  0 b. 2 x  y  12  0 c. 2 x  3 y  6  0 d. 4 x  3 y  4  0

35. Find the equation of a normal to the curve x 2  y 2  8 x  6 y  15  0 at ( 5 , 0 ).

a. x  3 y  5  0 b. 3x  y  15  0 c. 2 x  3 y  6  0 d. 3x  2 y  4  0

36. Find the equation of the tangent to the curve y 2  8 x  0 parallel to x  y  4  0.

a. x  y  2  0 b. x  y  2  0 c. x  y  2  0 d. x  y  2  0

37. The area of ellipse whose equation is 9 x 2  25 y 2  225 is ____________.

a. 3π b. 9π c. 5π d. 15π

38. The center of the hyperbola x 2  y 2  4 x  12 y  33  0 is __________.

a. ( 6 , 2 ) b. ( -6 , 2 ) c. (-2 , -6 ) d. ( 2 , 6 )

39. The center of the curve 100 x 2  64 y 2  300 x  256 y  81  0 is at point.

3 3 3 3
a. ( , 2) b. ( , 2) c. (2, ) d. (2,  )
2 2 2 2

40. The distance between points ( 8 , 1 ) and ( 0 , -5 ) is ___________.

a. 5 b. 4 c. 6 d. 10

41. The point ( 5 , y ) is 17 units from ( 6 , 2 ). Find y.

a. 6 and -2 b. 6 and 2 c. -6 and 2 d. – 6 and -2

42. What is the midpoint of ( 4 , - 4 ) and ( 6 , 8 )?

a. ( 10 , 4 ) b. ( 6 , 5 ) c. ( 5 ,2 ) d. ( -5 , 6 )

3 5 7 9
43. Find the slope of the line joining ( , ) and ( ,  ).
2 2 2 2
3 5 7 9
a. b. c. d.
2 2 2 2

44. The area of the triangle whose vertices are ( -6 , -8 ), ( 3 , - 5 ) and ( 4 , -2 ) is _____sq. units.
a. 18 b. 12 c. 24 d. none of these

1 4
45. Find the angle of two lines whose slopes are  and respectively.
2 5
2 1 13
a. Arctan b. Arctan c. Arctan d. none of these
5 5 6

46. A line passes through points ( -4 , -8 ) and ( 2 , 7 ). The equation of this line is ___________.
a. 5 x  3 y  4  0 b. 3x  2 y  4  0 c. 5 x  2 y  4  0 d. none of these

47. Which of this equation of x –axis?

a. x = 0 b. y = 0 c. x + y = 0 d. x = y

48. The slope and y - intercept of the line whose equation is 3x  4 y  8  0 are ____ respectively.
1 3
a.  and 8 b.  and 2 c. 4 and 8 d. 3 and 2
4 4

MAJORSHIP IN MATH
MR. BRYAN J. MADERSE, LPT, MAEd
WVSU
 4
49. A line with y-intercept of -7 and slope has the equation given below.
3
a. 3x  4 y  28  0 b. 4 x  3 y  21  0 c. 3x  4 y  28  0 d. 4 x  3 y  21  0

50. What is the distance from the x –axis to ( -7 , 4 )?

a. 7 b. 4 c. 3 d. 11

51. The slope of the line is -2. Find the equation of the line passing through ( 4 , -6 ).
a. 2 x  y  2  0 b. 3x  2 y  8  0 c. 3x  2 y  8  0 d. 2 x  y  2  0
52. Which is the equation of the line passing through ( -2 , 6 ) and is perpendicular to the y-axis?
a. y = -2 b. x = -2 c. y = -6 d. x = 6

53. Find the equation of the line passing through point ( -3 , -1 ) and parallel to the line 2 y  3x  5  0.
a. 3x  2 y  9  0 b. 2 y  3x  7  0 c. 3x  2 y  2  0 d. 2 y  3x  7  0

54. Find the equation of a line whose x-intercept is 4 and y-intercept is -6.
a. 3x  2 y  6 b. 3x  2 y  12 c. 4 x  6 y  1 d. 6 x  4 y  0

55. What is the x and y-intercept of the line 3x  8 y  24  0 ?

a. ( 24, 3 ) b. (3 , -8 ) c. ( -8 , 3 ) d. ( -8 , -3 )

56. The distance of points ( -6 , 3 ) from the line 2 x  y  4  0 is ____________ units.

19 3 5
a. b. c. d. 5
5 5 5

57. The equation of the circle with center at ( -4 , 1 ) and passing through ( 6 , -1 ) is.
a. x 2  y 2  8 x  3 y  22  0 c. x 2  y 2  6 x  y  2  0
b. x 2  y 2  4 x  3 y  37  0 d. NOTA

58. The center of the circle with an equation x 2  y 2  4 x  6 y  12  0 is at _____________.

a. ( -2 , 4 ) b. ( -2 , 3 ) c. ( 5 , 3 ) d. ( -2 , 5 )

59. The vertex of the curve x 2  8 x  4 y  8  0 is ______________.

a. ( -2 , 4 ) b. ( -2 , 8 ) c. ( -4 , -2 ) d. ( -2 , -2 )

60. Which among the equation is tangent to the curve at point ( 1 , 2 )?

a. 4 x  y  2 b. 2 x  y  1 c. 4 x  2 y  1 d. 4 x  y  1

61. Find the equation of the parabola with vertex at ( 5 , -2 ) and focus ( 5 , -4 ).
a. ( x  5) 2  8( y  2) c. ( x  5) 2  4( y  2)
b. ( x  5) 2  2( y  4) d. ( x  5)2  2( y  4)

x2 y 2
62. Find the area of the region bounded by the curve (sq. units)  1.
4 9
a. 36π b. 4π c. 6π d. 9π

63. What will be the equation of the parabola with vertex at ( 5 , -2 ) and focus ( 5 , -4 ).
a. y  4 x b. y  4 x c. x  4 y d. x  4 y
2 2 2 2

64. The center of the curve x  y  4 x  3 y  23  0 is at _____________.

2 2

a. ( -4 , 2 ) b. ( 3 , 1 ) c. ( -4 , 2 ) d. NOTA

MAJORSHIP IN MATH
MR. BRYAN J. MADERSE, LPT, MAEd
WVSU
 65. The center of the curve x 2  9 y 2  6 x  72 y  144  0 is at _____________.
a. ( 3 ,4 ) b. ( 4 , 3 ) c. ( -3 , -4 ) d. ( -4 , -3 )

MAJORSHIP IN MATH
MR. BRYAN J. MADERSE, LPT, MAEd
WVSU