PARABOLAS IN STANDARD POSITION y =p (0, p) (0, -p) (p. 0) (-p. 0) X =-P = 4px –4px x* = 4py x² = -4py Figure 10.4.6 To illustrate how the equations in Figure 10.4.6 are obtained, we will derive the equation for the parabola with focus (p, 0) and directrix x = -p. Let P(x, y) be any point on the parabola. Since P is equidistant from the focus and directrix, the distances PF and PD in Figure 10.4.7 are equal; that is, PF = PD (1)

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…