Question

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

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

Answer 1

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

Given the vertex and the focus of the parabola are $(0,4)$ and $(0,2)$.

From the question it is clear that the axis of the parabola is along the negative direction of the $y-$ axis.

So the equation of the parabola will be

$(x-0{)}^2=-4a(y-4)$.

Where $a$ is the distance between the focus and the vertex and $a=2$.

Now the equation of the parabola will be $x^2=-8(y-4)$ or, $x^2=-8y+32$ or, $x^2+8y=32$.