Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 9 Quadratic Relations and Conic Sections - 9.7 Solve Quadratic Systems - 9.7 Exercises - Quiz for Lessons 9.6-9.7 - Page 664: 4


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Work Step by Step

Given $9x^2-4y^2-36x-32y-64=0$ We can see that $a=9\\b=0\\c=4$ We will find the discriminant of the given equation $=b^2-4ac\\=0^2-4(9)(4)\\=144$ Since $144 \gt0$, the conic is a hyperbola. To graph the hyperbola, first complete the square in x. $9x^2-4y^2-36x-32y-64=0\\9(x^2-4x+4)-36-4(y+8y+16)+64=64\\9(x-2)^2-4(y+4)^2=36\\\frac{(x-2)^2}{4}-\frac{(y+4)^2}{9}=1$ From the equation, you can see that the center is at $(2,-4)$ and the vertices are at $(0,-4)$ or $(4,-4)$
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