## Parabola Questions and Answers Part-4

1. Equation of the normal at a point on the parabola $y^{2}=36x$   , whose ordinate is three times its abscissa is
a) 2x + 3y + 44 = 0
b) 2x – 3y + 44 = 0
c) 2x + 3y – 44 = 0
d) 2x – 3y = 0

Explanation:

2. If a,b> 0 , then the angle of intersection of two parabolas $y^{2}=a^{3}x$   and $x^{2}=b^{3}y$   at a point other than the origin is
a) $\tan^{-1}\left(\frac{3ab}{2\left(a^{2}+b^{2}\right)}\right)$
b) $\tan^{-1}\left(\frac{ab}{\left(a^{2}+b^{2}\right)}\right)$
c) $\tan^{-1}\left(\frac{a^{2}+b^{2}}{ab}\right)$
d) $\tan^{-1}\left(\frac{3\left(a^{2}+b^{2}\right)}{2ab}\right)$

Explanation:

3. O is the vertex and LL' is the latus rectum of the parabola. Let P be a point on the parabola and Q be a point on the axis of the parabola such that $OPQ =\frac{\pi}{2}.$     Suppose length of the projection of PQ on the axis of the parabola be $\alpha$  , then $\alpha -\mid LL'\mid$    equals
a) a
b) 2a
c) -a
d) 0

Explanation:

4. An equation of the latus rectum of the parabola $x^{2}+4x+2y=0$    is
a) $y=-\frac{3}{2}$
b) $y=\frac{2}{3}$
c) $y=\frac{3}{2}$
d) $y=-\frac{2}{3}$

Explanation:

5. $y=\left(x-11\right) \cos\theta-\cos3\theta$      is a normal to the parabola $y^{2}=16x$   for
a) only one value of $\theta$
b) two values of $\theta$
c) all values of $\theta$
d) no value of $\theta$

Explanation:

6. If the normals are drawn from the point P(5, b) to the parabola $y^{2}=4x$  , then
a) there are three normal if –2 < b < 2
b) there id exactly one normal with positive slope if b< -2
c) there is exactly one normal with negative slope if b > 2
d) All of the Above

Explanation:

7. Equations (s) of the commom tangent (s) to the parabola and $y^{2}=4x$   is $x^{2}+4y^{2}=8$    are
a) x + 2y + 4 = 0
b) x + 2y – 4 = 0
c) x – 2y – 4 = 0
d) Both a and c

Explanation:

8. A circle with centre (a,0) touches the directrix of the parabola $y^{2}=4ax.$   Tangents to the parabola at points of intersection of the parabola and the circle are.
a) x + y + a = 0
b) x + y – a = 0
c) x – y + a = 0
d) Both a and c

Explanation:

9. The points of contact of tangents from (-3,5) to the parabola $y^{2}=4\left(x-3\right)$    are
a) (4, 2)
b) (4, –2)
c) (39, 12)
d) Both b and c

10. If length of focal chord of the parabola $y^{2}=4ax$   at a distance 2ab from the vertex is ac, then
a) $0< b\leq\frac{1}{2}$
b) $c\geq 4$
c) $b^{2}c=1$