Example 1: Vertical Parabola

Find an equation for the vertical parabola with directrix y = -1 and focus F(0, 1) (Figure 5.4.6).

Figure 5.4.6

Given a point P(x, y), the perpendicular from P to the directrix is a vertical line of length. Thus

distance from P to directrix =

Also,

distance from P to focus =

The point P lies on the parabola exactly when these distances are equal,