Parabola and Ellipse — Class 12 Mathematics PYQs

In the parabola $y^2=8x$, the focal distance of a point $P$ lying on it is $8$ units. Which of the following statements is/are correct?

1. The coordinates of $P$ can be $(6,4\sqrt{3})$.
2. The perpendicular distance of $P$ from the directrix of parabola is $8$ units.

Select the correct answer using the code given below:

What is the eccentricity of the ellipse if the angle between the straight lines joining the foci to an extremity of the minor axis is $90^{\circ }$?

Consider the following for the next two (02) items that follow :

A parabola passes through $(1,2)$ and satisfies the differential equation $\frac{dy}{dx}=\frac{2y}{x}$, $x>0,y>0$.

What is the directrix of the parabola ?

Consider the following for the next two (02) items that follow :

A parabola passes through $(1,2)$ and satisfies the differential equation $\frac{dy}{dx}=\frac{2y}{x}$, $x>0,y>0$.

What is the length of latus rectum of the parabola ?

Consider the following for the next two (02) items that follow :

$P(x,y)$ is any point on the ellipse $x^2+4y^2=1$. Let $E,F$ be the foci of the ellipse.

What is $PE+PF$ equal to?

Consider the following for the next two (02) items that follow :

$P(x,y)$ is any point on the ellipse $x^2+4y^2=1$. Let $E,F$ be the foci of the ellipse.

Consider the following points :

1. $\left(\frac{\sqrt{3}}{2},0\right)$
2. $\left(\frac{\sqrt{3}}{2},\frac{1}{4}\right)$
3. $\left(\frac{\sqrt{3}}{2},-\frac{1}{4}\right)$

Which of the above points lie on latus rectum of ellipse?

What is the equation of directrix of parabola $y^2=4bx$, where $b<0$ and $b^2+b-2=0$ ?

Consider the following in respect of the equation $\frac{x^2}{24-k}+\frac{y^2}{k-16}=2$.

1. The equation represents an ellipse if $k=19$.
2. The equation represents a hyperbola if $k=12$.
3. The equation represents a circle if $k=20$.

How many of the statements given above are correct ?

What is the equation of the parabola with focus $(-3,0)$ and directrix $x-3=0$ ?

What is the distance between the foci of the ellipse $x^2+2y^2=1$ ?