Chapter 10.5, Problem 10E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# Find an equation of the parabola. Then find the focus and directrix.10.

To determine

To Find: The equation of the parabola, focus and the directrix by using figure (1).

Explanation

Given:

By referring the figure (1), we can find the value of vertex.Â  Then the vertex is (2,âˆ’2).

Calculation:

By referring the figure (1) graph is open up upward in the direction of y, so the equation,

x2=4py (1)

And the focus of the parabola is to be (0,p).

Compute the value of the p in equation below.

(xâˆ’h)2=4p(yâˆ’k) (2)

Substitute the value âˆ’2 for h and 2 for k in the equation (1).

(xâˆ’h)2=4p(yâˆ’k)(xâˆ’2)2=4p(yâˆ’(âˆ’2))

(xâˆ’2)2=4p(y+2) (3)

Substitute the value 0 for x and 0 for y in the equation (3).

(0âˆ’2)2=4p(0+2)4=8pp=12

Compute the focus of the parabola:

Focus=(h,k+p)

Substitute the value 12 for pâˆ’2 for h and 2 for k

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