Find the equation in the standard form of the parabola descr

Find the equation in the standard form of the parabola described below. The focus has coordinates (0, - 9/2), and the equation of the directrix is y - 9/2. The equation in the standard form of the parabola is.

Solution

Let (x,y) be any point on the parabola. Find the distance between (x,y) and the focus. Then find the distance between (x,y) and directrix. Equate these two distance equations and the simplified equation is equation of the parabola.

sqrt( (x -0)^2 + (y +9/2)^2 ) = ( y- 9/2)

x^2 + (y +9/2)^2 = (y-9/2)^2

x^2 + y^2 + 81/4 + 9y = y^2 +81/4 -9y

x^2 = -18y ( equation of parabola)