Find the standard form of the equation of the parabola with

Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.

Solution

Given that :

Focus = (0,-2) and directix at y = 2

therefore the vertex, exactly between the focus and directrix, must be at (h, k) = (0, 0).

therefore equation of parabola

Let any point on parabola (x,y) and distance between focus to the point on parabola and to the point on directix are equal

(y-2)² + (x-x)² = (x-0)²+(y-(-2))²

y² +4 -4y = x²+ y²+4y+4

8y = x²

x²=8y

Answer: