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)
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)
Chapter4: Rational Functions And Conics
Section4.3: Conics
Problem 99E
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Derive the equation x² = 4py in Figure 10.4.6.
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