Objective 1 Identify the Focus and Directrix of a Parabola F

Objective 1: Identify the Focus and Directrix of a Parabola For Exercises 15-22, a model of the form x^2 = 4py or y^2 = 4px is given. a. Determine the value of p. b. Identify the focus of the parabola. c. Write an equation for the directrix. (See Example 1) x^2 = 24y x^2 = 12y y^2 = 48x x^2 = -5y -x = y^2 -3x = y^2

Solution

22)

a) given -3x=y²

=>y²=-3x

=>4p =-3

=>p=-3_/4

(b)

focus (p,0)

focus=(-3_/4,0) or (-0.75,0)

(c)

equation of directrix , x=-a

=>x=-(-3_/4)

=>x=3_/4 or x=0.75