Question

A parabola has its vertex at (2, 2), and the equation of its directrix is y = 2.5. The equation that represents the parabola is

Answer 1

Vertex = (2,2)
Directrix = y=2.5

line of symmetry is the Y value in the vertex = 2

subtract directrix from Y value of vertex
2 - 2.5 = -0.5
focus = 2, (2-.5) = (2,1.5)

now distance for a point

2.5 -y = sqrt(x-2)^2 +y-1.5)^2)

(2.5-y)^2 = (x-2)^2 + (y-1.5)^2

6.25 - 5y +y^2 = (x-2)^2 + y^2 -3y +2.25


(x-2)^2 = -2(y-2)