4. Classify the following as an ellipse, hyperbola, or parabola and sketch a graph like we have done in class (complete the square to get the more useful version of the equation): a. 9x +4y-36x- 24y +36 = 0

4. Classify the following as an ellipse, hyperbola, or parabola and sketch a graph like we have done in class (complete the square to get the more useful version of the equation): a. 9x +4y-36x- 24y +36 = 0

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter7: Conic Sections And Quadratic Systems

Section7.2: The Ellipse

Problem 62E

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Question

4. Classify the following as an ellipse, hyperbola, or parabola and sketch a graph like we
have done in class (complete the square to get the more useful version of the equation):
a. 9x +4y-36x- 24y +36 = 0

Expert Solution

Step 1

Consider the equation,

$9 x^{2} + 4 y^{2} - 36 x - 24 y + 36 = 0$

Step 2

To write the equation in standard form by completing the square method,

$\begin{matrix} 9 x^{2} + 4 y^{2} - 36 x - 24 y + 36 = 0 \\ 9 x^{2} - 36 x + 4 y^{2} - 24 y = - 36 \\ 9 (x^{2} - 4 x + {(2)}^{2} - {(2)}^{2}) + 4 (y^{2} - 6 y + {(3)}^{2} - {(3)}^{2}) = - 36 \\ 9 [{(x - 2)}^{2} - 4] + 4 [{(y - 3)}^{2} - 9] = - 36 \end{matrix}$