   Chapter 10.1, Problem 22E

Chapter
Section
Textbook Problem

# Finding the Standard Equation of a Parabola In Exercises 17-24, find the standard form of the equation of the parabola with the given characteristics.Directrix: y = − 2 : endpoints of latus rectum are ( 0 ,   2 ) and ( 8 ,   2 ) .

To determine

To calculate: The equation of parabola with the directrix y=2 and end points of latus rectum (0,2) and (8,2).

Explanation

Given:

The directrix y=2 and end points of latus rectum (0,2) and (8,2) of parabola.

Formula used:

The standard equation of parabola is, (xh)2=4p(yk)

Calculation:

Since the given parabola has y=2 as the directrix therefore the parabola is a U-shaped parabola of the type (xh)2=4p(yk) where (h,k) is the vertex and (h,k+p) is the focus.

The equation of directrix of the parabola is, y=kp

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