Question

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

• A. $x^2+8y=32$
• B. $y^2+8x=32$
• C. $x^2-8y=32$
• D. $y^2-8x=32$

Answer 1

The correct option is A $x^2+8y=32$

General equation of parabola whole vertex are $(h,x)$ are $(x-h{)}^2=-ya(y-x)$

given vertex = $(0,4)$

& focus = $(0,2)$

It is clear that vertex & focus lies on the tide of y axis $\therefore$ It open down words

i.e.,

$(x-0{)}^2=-4\times 2(y-4)$

$\Rightarrow x^2=-8y+32$

$\therefore x^2+8y-32$ is required equation of parabola.