   Chapter 12.CR, Problem 45E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

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

# 43-54 ■ Indentifying and Graphic a conic Determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is ellipse, find the center foci and vertices. If it is parabola, find the vertex, focus, and directrix. If it is hyperbola, find the center, foci, vertices and asymptotes. Then sketch the graph of the equation. If the equation has no graph, explain why.45. x 2 − y 2 + 144 = 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. Sketch the graph of the equation. Mention the reason, if equation has no graph.

Explanation

Given:

x2y2+144=0

Approach:

Rearrange the terms into the equation of conic and compare the equation with the standard equations of conics.

Calculation:

Rearrange the terms of equation, as follows

x2y2+144=0

x2y2=144

y2144x2144=1

Above equation is an equation of a vertical hyperbola. Compare the above equation with the standard equation of the hyperbola (yk)2a2(xh)2b2=1.

Center of the hyperbola will be (h,k)=(0,0). Since a2=144 and b2=144, then a=12 and b=12. So c=a2+b2=144+144=122

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