Use the Distance Formula to write an equation of the parabola with focus F(0,4) and directrix y=−4

Question

Use the Distance Formula to write an equation of the parabola with focus F(0,4) and directrix y=−4

The equation is y=?

Answer 1

The distance from the focus to any point on the parabola is equal to the distance from the point to the directrix.

distance from (x,y) to focus = distance from (x,y) to directrix

√ (x-0)² + (y-4)² = √(x-x)² + (y-(-4))²

√ x² + (y-4)² = √(y+4)²

x² + (y-4)² = (y+4)²

x² + y² - 8y + 16 = y² + 8y + 16

x² = 16y

y = (1/16)x²

Hope this helps!