Question

I. If vertex $(0,0)$ and focus $(3,0)$, then the equation of parabola is $y^2=-12 x$.
II. If vertex $(0,0)$ and focus $(-2,0)$, then the equation of parabola is $y^2=-8 x$.

• 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: (C)

I. Given, vertex $=(0,0)$
Focus $=(3,0)$
Since, vertex is $(0,0)$ and focus lies on positive direction of $X$-axis. Hence, equation of parabola will be of the form $y^2=4 a x$ with $a=3$
Hence, required equation is
$ y^2 =4 \times 3 x$
$\Rightarrow y^2 =12 x$
II. Given, vertex $=(0,0)$
Focus $=(-2,0)$
Since, vertex is $(0,0)$ and focus lies on the negative direction of X-axis. Hence, equation of parabola will be of the form
$y^2=-4 a x \text { with } a=2$
Hence, required equation is
$y^2 =-4(2) x $
$ =-8 x$