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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

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

10. Chapter 10.5, Problem 10E, 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).

Multivariable Calculus, Chapter 10.5, Problem 10E

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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