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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

10-12 ■ Determine whether the equation represents an ellipse, a parabola, or a hyperbola. If the graph is an ellipse, find the center, foci, and vertices. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

16 x 2 + 36 y 2 96 x + 36 y + 9 = 0

To determine

To find:

Whether the equation represents an ellipse, a parabola, or a hyperbola. If the graph is an ellipse, find the center, foci, and vertices. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

Explanation

Given:

16x2+36y296x+36y+9=0

Approach:

Complete the square and rearrange the terms into the equation of conic. Then compare the equation with the standard equation of that conic.

Calculation:

Make the perfect square in the given equation, as follows

16x2+36y296x+36y+9=0

16(x26x)+36(y2+y)+9=0

16(x26x+9)+36(y2+y+14)1449+9=0

16(x3)2+36(y+12)2=144

(x3)29+(y+12)24=1

Above equation is an equation of an ellipse. Compare the above equation with the standard equation of the shifted ellipse (xh)2a2+(yk)2b2=1.

Center of the ellipse will be (h,k)=(3,12)

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Chapter 12 Solutions

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