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# 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 }= -x^{2}

y^{2 }- 10y + 25 - y^{2 }- 10y - 25 = -x^{2}

-20y = -x^{2}

20y = x^{2}

y = x^{2}/20

The quadratic equation created is y = x^{2}/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 = x^{2} /20.

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