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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

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Chapter
Section
BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 8.CR, Problem 29CR
Textbook Problem
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For Problems 25 30 , find the equations of the asymptotes of each hyperbola.

25 x 2 + 100 x 4 y 2 + 24 y 36 = 0

To determine

To find:

The equations of the asymptotes of the given hyperbola

Explanation of Solution

Given:

The given equation of the hyperbola is,

25x2+100x4y2+24y36=0

Approach:

The general equation of the hyperbola not symmetric to both axes is,

A(xh)2B(yk)2=C

Where, A, B and C are nonzero real numbers and C is a constant.

To find the equation for the asymptotes replace the constant term of A(xh)2B(yk)2=C with 0 and solve for y.

A(xh)2B(yk)2=0

Calculation:

Consider the given equation of the hyperbola.

25x2+100x4y2+24y36=0

Express the above equation in the general form by completing the square.

25x2+100x4y2+24y36=025(x2+4x)4(y26y)=3625(x2+4x+22)4(y26y+(3)2)=36+25(22)4(3)225(x2+4x+4)4(y26y+9)=36+10036

Simplify the above equation.

25(x+2)24(y3)2=100(1)

Compare the above equation with A(xh)2B(yk)2=C

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