   Chapter 10.5, Problem 33E

Chapter
Section
Textbook Problem

# Find an equation for the conic that satisfies the given conditions.33. Parabola, focus (−4, 0), directrix x = 2

To determine

To Find: The equation for the conic using the focus (4,0) and directrix x=2 of the parabola.

Explanation

Given:

Focus is (0,0) and directrix y=6 of the parabola.

Calculation:

Compute the distance from the focus to the directrix.

2p=focusofxaxisdirectrix

Substitute 4 for focus of y axis and 2 for directrix in above equation.

2p=422p=6p=62p=3

Compute the value of h using the below focus equation.

Focus=(h+p,k)(4,0)=(h+p,k)

The value of k=0 .

(h+p)=4 (1).

Substitute the value 3 for p in equation (1).

(h+(3))=4h=4+3h=1

The value of p is 3 then p<1

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