Analytic Geometry 2
Analytic Geometry 2
Analytic Geometry 2
2 2
4. Find the eccentricity of the curve 9x - 4y - 36x + 8 y = A. (2, -5) C. (-5, -1)
4. B. (-2, 3) * D. (1, 2)
A. 1.80 C. 1.90
B. 1.70 D. 1.60
Find the focus of the parabola x 2 16 y 3
2
7.
5. Find the location of the vertex of the hyperbola A. (-2, 1) C. (-2, -1) *
16y 2 9x 2 36x 96y 36 0 B. ( 2, 1 ) D. ( 1, 2 )
A. (1, 1) and (3, 6) C. (4, 0) and (5,
8. Find the equation of the directrix of the parabola
6)
x 2 16 y 3
2
B. (2, 0) and (2, -6) * D. (1, 0) and (4, -
6) A. y = 5 C. y = -4
B. y = 7 * D. y = -6
6. Find the equation of the hyperbola with vertices at (-4,2)
and (0,2) and foci at (-5,2) and (1,2). 9. Find the equation of the parabola with vertex at (5, -2)
and focus at (5, -4)
III. Parabola
A. x 2 10x 8y 41 0 * C. x 2 8x 4y 36 0
7. Compute the focal length and the length of latus rectum B. x 2 5x 6y 45 0 D. x 2 12x 10y 40 0
2
of parabola y + 8x – 6y + 25 = 0 .
A. 2 , 8 C. 4 , 16 10. Find the area enclosed by the parabola y 2 8 x and the
B. 16 , 64 D. 1 , 4
latus rectum.
8. Find the equation of the parabola with vertex at (5, -2) and A. 32/3 sq. units * C. 41/2 sq. units
focus at (5, -4) B. 29/4 sq. units D. 33/2 sq. units
A. x 2 10x 8y 41 0 * C. x 2 8x 4y 36 0
11. Find the latus rectum of the parabola y 2 8 x
B. x 2 5x 6y 45 0 D. x 2 12x 10y 40 0 A. 8 * C. 16
B. 11 D. 10
9. Find the equation of a parabola with axes vertical and
passing through (0, 0), (1, 0) and (5, -20). 12. The focus of the parabola y 2 4x is at:
A. x 2 x y 2 0 C. x x 2 y 2 0 A. (4, 0) * C. (1, 0)
B. x2 - x + y 0 * D. x x y 0 B. (0, 4) D. (0, 1)
10. ME Board Problem 13. Find the equation of a parabola with axes vertical and
An arch 18 m high has the form of parabola with a passing through (0, 0), (1, 0) and (5, -20).
vertical axis. The length of a horizontal beam placed A. x 2 x y 2 0 C.
across the arch 8 m from the top is 64 m. Find the width x x2 y 2 0
of the arch at the bottom.
A. 86 m C. 96 m B. x2 - x + y = 0 * D.
B. 106 m D. 76 m xxy 0
IV. Polar coordinate system 14. Find the equation of a parabola having a directrix y 4
with its axis along the y-axis and vertex at the origin.
11. What is the polar equation of a circle of radius 3 units and
center at (3,0)? A. x 2 16y * C. x 2 4y
2
B. y 2 16x D. y 2 4x
12. Determine the length of the latus rectum of the curve rcos
θ - 4cos θ = 16sin θ 15. A cable suspended form supports that are the same
height and 600 ft. apart has sag of 100 ft. If the cable
PRACTICE PROBLEMS hangs in the form of a parabola, find its equation taking
the origin at the lowest point.
PROBABLE PROBLEMS: Choose the best answer.
A. x 2 900y * C. y 2 900x
1. Find the center of the curve 2x 2 8 x 2y 2 12y 1
B. x 2 400y D. y 2 400 x
ANALYTIC GEOMETRY 02
MAGNIFIED REVIEW for MECHANICAL ENGINEERS – BUTUAN CITY MATHEMATICS
19. Find the vertex of the parabola having its focus at (7, -3)
and its directrix y = 2.
A. (7, -1) * C. (-4, 2)
B. (6, -2) D. (3, -5)
25. A point moves so that the sum of its distances from the
point (-2, 2) and (4, 2) is 8. Find the eccentricity of its
locus.
A. 0.75 * C. 0.60
B. 0.80 D. 0.50