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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

Conjugate Hyperbolas

x 2 a 2 y 2 b 2 = 1 and x 2 a 2 y 2 b 2 = 1

are said to be conjugate to each other.

(a) Show that the hyperbolas r2 - 4y2 + 16 = fl and 4y2 — r2 + 16 = 0 are conjugate to each other, and sketch their graphs or the same coordinate axes.

(b) What do the hyperbolas of part (a) have in common?

(c) Show that any pair of conjugate hyperbolas have the relationship you discovered in part (b).

To determine

(a)

To show:

The hyperbolas x24y2+16=0 and 4y2x2+16=0 are conjugate to each other and sketch the graph.

Explanation

Approach:

The standard form of conjugate hyperbolas is,

x2a2y2b2=1 and x2a2y2b2=1

Calculation:

Consider the given equation.

x24y2+16=0

Write the above equation in standard form.

x216y24=1 ……(1)

Consider the given equation.

4y2x2+16=0

Write the above equation in standard form

To determine

(b)

To find:

The common part of hyperbolas x24y2+16=0 and 4y2x2+16=0.

To determine

(c)

To show:

The same relationship is satisfied for any pair of conjugate parabolas.

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