PARABOLA DPP-1
Parabola Definition and Standard Equations
1. Curve 16 x2 8xy y 2 74 x 78 y 212 0 represents
(A) Parabola (B) Hyperbola (C) Ellipse (D) None of these
2. The equation px2 4 xy y 2 px 3 y 2 0 represents a parabola if value of p is
(A) 0 (B) – 4 (C) 4 (D) 1
3. The equation of 2 x2 3 y 2 8x 18 y 35 k represents
(A) No locus if k 0 (B) An ellipse, if k 0 (C) A point if, k 0 (D) A hyperbola, if k 0
4. The equation of parabola whose focus is (5, 3) and directrix is 3x 4 y 1 0 , is
(A) (4 x 3 y)2 256 x 142 y 849 0 (B) (4 x 3 y)2 256 x 142 y 849 0
(C) (3x 4 y)2 142 x 256 y 849 0 (D) (3x 4 y)2 256 x 142 y 849 0
5. The equation of the locus of a point which moves so as to be at equal distances from the point (a, 0) and the y-axis is
(a) y 2 2ax a 2 0 (b) y 2 2ax a 2 0 (c) x2 2ay a 2 0 (d) x2 2ay a 2 0
6. The length of the latus rectum of the parabola 169{( x 1)2 ( y 3)2 } (5x 12 y 17)2 is
(A) 7/13 (B) 14/13 (C) 28/13 (D) 32/13
7. Length of the latus rectum of the parabola (a b )( x y ) (bx ay ab) is
2 2 2 2 2
ab ab 3ab 2ab
(A) (B) (C) (D)
2 a b 2 2
a b
2 2
2 a b 2 2
a 2 b2
8. The correct order of eccentricities of parabola, ellipse, hyperbola and rectangular hyperbola respectively is
2 2 2 2
(A) ,1, 3, 2 (B) 1, , 2, 3 (C) 1, , 3, 2 (D) 1, 3, , 2
3 3 3 3
9. If the parabola y 2 4ax passes through the point (- 3, 2), then the length of its latus rectum is
(A) 1/3 (B) 4/3 (C) 5/3 (D) 4
u2 u 2
u2
10. The length of the latus-rectum of the parabola whose focus is sin 2 , cos 2 and directrix is y , is
2g 2g 2g
u2 u2 2u 2 2u 2
(A) cos 2 (B) cos 2 (C) cos 2 2 (D) cos 2
g g g g
11. The equation of latus rectum of a parabola is x y 8 and the equation of the tangent at the vertex is x y 12 , then
length of the latus rectum is
(a) 4 2 (b) 2 2 (c) 8 (d) 8 2
12. The co-ordinates of the extremities of the latus rectum of the parabola 5 y 2 4 x are
(A) (1/ 5, 2 / 5), (1/ 5, 2 / 5) (B) (1/ 5, 2 / 5), (1/ 5, 2 / 5) (C) (1/ 5, 4 / 5), (1/ 5, 4 / 5) (D) None of these
13. The ends of latus rectum of parabola x2 8 y 0 are
(a) (–4, –2) and (4, 2) (b) (4, –2) and (–4, 2) (c) (–4, –2) and (4, –2) (d) (4, 2) and (–4, 2)
14. Directrix of a parabola is 5x 12 y 7 and focus is at (2, 3). It latus rectum is
(A) 4 (B) 5 (C) 6 (D) 7
15. The focus and vertex of parabola are 2,1 and 1,5 then Its latus rectum is
(A) 20 (B) 10 (C) 5 (D) 40
16. If the focus a parabola is (- 2, 1) and the directrix has the equation x y 3 then the vertex is
(A) (- 1, 2) (B) (2, - 1) (C) (0, 3) (D) (- 1, 1/2)
17. If directrix and vertex of a parabola are 2 x y 4 0 and (5, 1) respectively, then incorrect statement is
(A) Its focus is (7, 0) (B) Its axis is x 2 y 7 0
(C) Equation of tangent at vertex is 2 x y 9 0 (D) length of latus rectum is 5
18. A point on a parabola y 2 8x whose focal distance is 8 is
(A) 6, 4 3 (B) 6, 4 3 (C) 6, 4 3 (D) None of these
19. The focal distance of a point on the parabola y 16 x whose ordinate is twice the abscissa, is
2
(a) 6 (b) 8 (c) 10 (d) 12
1
20. A point on a parabola y 2 6 x whose focal distance is 15 is
27 27 27 27
(A) ,9 (B) , 9 (C) , 9 (D) , 9
2 2 2 2
21. A point on a parabola x 2 x 8 y 1 0 whose focal distance is 10 is
2
(A) 9,8 (B) 7,8 (C) 7, 8 (D) 9, 8
22. The curve described parametrically by x t t 1, y t t 1 represents
2 2
(A) Pair of straight lines (B) Ellipse (C) Parabola (D) Hyperbola.
23. Which one of the following equations parametrically represents equation to a parabolic profile?
t
(A) x 3cos t ; y 4sin t (B) x 2 2 2 cos t ; y 4 cos 2
2
t t
(C) x tan t ; y sec t (D) x 1 sin t ; y sin cos
2 2
2
24. The points of intersection of the curves whose parametric equations are x t 2 1, y 2t and x 2s, y is given by
s
(A) (1, 3) (B) (2, 2) (C) (–2, 4) (D) (1, 2)
25. The angle subtended by the double ordinate of length 8a of the parabola y 2 4ax is
(a) /3 (b) /4 (c) /2 (d) 2/3
26. AB is a double ordinate of the parabola y 4 x. The locus of its point of trisection is
2
(A) 4 y 2 9 x (B) 9 y 2 4 x (C) 9 y 2 4 x 0 (D) 4 y 2 9 x 0
27. If on a given base, a triangle be described such that the sum of the tangents of the base angles is a constant, then the locus
of the vertex is:
(A) a circle (B) a parabola (C) an ellipse (D) a hyperbola
28. The length of latus rectum of parabola represents by the equation x2 2 xy y 2 16 x 16 y 32 0 is
(A) 4 (B) 8 2 (C) 4 2 (D) 2 2
29. The vertex parabola represents by the equation 3 x 4 y 1 10 4 x 3 y 7 0 is
2
(A) (2, 5) (B) (3, 2) (C) (1, 1) (D) (1, 1)
30. The axis of parabola is along the line x y. The distance of its vertex and focus from origin are 2 and 2 2
respectively and both lies in first quadrant, then the equation of parabola is
x y x y 2 x y x y 2 x y 4 x y 2 (d) x y 8 x y 2
2 2 2 2
(a) (b) (c)
ANSWERS
1 2 3 4 5 6 7 8 9 10
A C C D A C D C B A
11 12 13 14 15 16 17 18 19 20
D B C C A A D A B D
21 22 23 24 25 26 27 28 29 30
C C B B C B B B C D
