The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is

Solution:

Given directrix of y = -5 and focus (0,5)

from any point (x, y) on the parabola the focus and directrix are equidistant

We are using distance formula √{(x - 0)² + (y - 5)²} = |y + 5|

Applying square on both sides

(x)² + (y - 5)² = (y + 5)²

(y - 5)² - (y + 5)² = -x²

y² - 10y + 25 - y² - 10y - 25 = -x²

-20y = -x²

20y = x²

y = x²/20

The quadratic equation created is y = x²/20

The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is

Summary:

The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is y = x² /20.