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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

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. images

To determine

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

images

Explanation

Given:

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

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.

(xh)2=4p(yk) (2)

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

(xh)2=4p(yk)(x2)2=4p(y(2))

(x2)2=4p(y+2) (3)

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

(02)2=4p(0+2)4=8pp=12

Compute the focus of the parabola:

Focus=(h,k+p)

Substitute the value 12 for p2 for h and 2 for k

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