Use the distance formula to write an equation of the parabola with focus f(0, −10)f(0, −10) and directrix y=10y=10.

Distance formula: the distance, d, between two coordinates  and  is given bygeometric definition of a parabola:   set of points on a plane that are the same distance from a focus point and a directrix line.let be the distance between the point  and the focus point at . using the distance formula: let be the distance between the  point  and  the directrix at , which is a horizontal line. when talking about this distance between a point and a horizontal line, we only care about the vertical distance. there is a point on the horizontal line that would share the same x-coordinate. sothese two distances must be equal: if we square both sides to get rid of the square roots both sides have  and 100; if we subtract those two from both sides of the equation: so