Question

If $(0,6)$ and $(0,3)$ are respectively the vertex and focus of a parabola, then its equation is:

• A. $x^2+12y=72$
• B. $x^2-12y=-72$
• C. $y^2-12x=72$
• D. $y^2+12x=72$

Answer 1

The correct option is A $x^2+12y=72$

Clearly the axis of the parabola is $x=0$

So the parabola is of the form $(x-0{)}^2=4a(y-6)$

Now the length of latus rectum $=4a=4\times$ the distance between focus and vertex $=4\times 3=12$

Hence the parabola is $x^2=-12(y-6)$