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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

Identify the type of conic section whose equation is given and find the vertices and foci.

28. y2 − 2 = x2 − 2x

To determine

To Find: The type of conic section, vertices, and foci for the equation y22=x22x .

Explanation

Given:

The equation is as follows.

y22=x22x (1)

Rewrite the equation.

y2x2+2x+1=21

Factorize the above equation as below.

y2(x1)2=1

Divide the above equation by (1).

y21(x1)21=11

y21(x1)21=1 (2)

Then, compare the equation (2) with the standard equation of hyperbola.

y2a2x2b2=1 (3)

Therefore, the type of conic section is hyperbola_ .

Calculation:

Compute the center of the hyperbola using the equation.

(yk)2a2+(xh)2b2=1(y0)21+(x(1))21=1

Therefore, the center of the hyperbola (h,k) is (0,1) .

Substitute the value 1 for a2 and 1 for b2 in equation (3).

a2=1a=1

b2=1b=1

Compute the vertices

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