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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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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.

Foci ( 0 , ± 1 ) , length of transverse axis: 1

To determine

To find:

The equation for the hyperbola when the foci are (0,±1), and the length of the transverse axis is 1.

Explanation

Given:

The foci are (0,±1), and the length of the transverse axis is 1.

Approach:

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

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

b2=c2a2 ...(2)

l=2a ...(3)

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

Calculation:

Since,

foci are (0,±1).

Use the midpoint formula to find h and k.

(h+h2,k+c+kc2)=(0+02,112)(h,k)=(0,0)

So, h=0, k=0

Since, the length of transverse axis is 1. Then,

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