Question

If the points (0,4) and (0,2) are respectively the vertex and focus of the parabola, then find the equation of the parabola.

Answer 1

Given that the coordinates,vertex of the parabola (0,4) and focus of the parabola (0,2)

By definition of the parabola, PB=PF

$\Rightarrow \left|\frac{0+y-6}{\sqrt{0+1}}\right|=\sqrt{(x-0{)}^2+(y-2{)}^2}$

$\Rightarrow |y-6|=\sqrt{x^2+y^2-4y+4}$

$\Rightarrow x^2+y^2-4y+4=y^2+36-12y$

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