Question

I. If focus $(6,0)$ and directrix $x=-6$, then the equation of parabola is $y^2=24 x$.
II. If focus $(0,-3)$ and directrix $y=3$, then the equation of parabola is $x^2=12 y$.

• A. Both I and II are true
• B. Only I is true
• C. Only II is true
• D. Both I and II are false

Answer 1

Answer: (B)

I. Given, focus $(6,0)$ and directrix $x=-6$
Here, we see that in focus $x$-coordinate is positive and $y=$ coordinate is zero.
Sn, focus lies on the positive direction of $X$-axis i.e., equation of parabola will be of the form $y^2=4 a x$ with $a=6$.
Hence, required equation is
$y^2-4 \times 6 x \rightarrow y^2-24 x$
II. Given, focus $=(0,-3)$ and directrix $y=3$
Since, focus lies on the negative direction of $Y$-axis i.e., equation of parabola will be of the form $x^2=-4$ 4ay with $a=3$.
Hence, required equation is
$x^2=-4(3) y \Rightarrow x^2=-12 y$