Question

If the focus and vertex of parabola are the points $(0,2)$ and $(0,4)$ respectively, then its equation is

(a) $y^2=8 x+32$

(b) $y^2=-8 x+32$

(c) $x^2+8 y=32$

(d) $x^2-8 y=32$

Answer 1

SOLUTION — Since, the focus and vertex of the parabola are on $y$-axis, therefore its directrix is parallel to $x$-axis and the axis of parabola is $y$-axis.

Let equation of directrix be $y=k$.

$\therefore \quad \frac{k+2}{2}=4 \Rightarrow k=6$

$\therefore$ Equation of directrix is $y=6$

$\therefore$ By definition of Parabola,

$\Rightarrow \quad \begin{array}{rlrl}(x-0)^2+(y-2)^2 =(y-6)^2 \\x^2+8 y =32\end{array}$

So, The correct option of this question will be (C).