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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Chapter
Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

37-50 Finding the equation of a Hyperbola Find an equation for the hyperbola that satisfies the given conditions.

Asymptotes y = ± x , hyperbola passes through ( 1 , 2 )

To determine

To find:

The equation of the hyperbola with the asymptotes are y=±x, and it passes through (1,2).

Explanation

Approach:

The general equation of a hyperbola with y-axis as transverse axis is given by

(yk)2a2(xh)2b2=1...(1)

And b2=c2a2...(2)

The asymptotes are given by,

y=±ab(xh)+k...(3)

Here, a is the transverse axis, b is the conjugate axis, c is the focus, and (h,k) is the center of the hyperbola.

Calculation:

Compare y=±x with the equation (3), we get

h=0, k=0,

ab=±1

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