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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

69–72 Identifying a Conic An equation of a conic is given.

(a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the x y term. (c) Sketch the graph.

9 x 2 + 24 x y + 16 y 2 = 25

To determine

(a)

To find:

Whether the graph of the equation 9x2+24xy+16y2=25 is a parabola, an ellipse, or a hyperbola using the discriminant.

Explanation

Approach:

The graph of the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 is

1. a parabola if B24AC=0,

2. an ellipse if B24AC<0,

3. a hyperbola if B24AC>0.

Here, the quantity B24AC is called the discriminant of the equation

To determine

(b)

To find:

The equation of the conic after eliminating the xy term using the rotation of axis.

To determine

(c)

To sketch:

The graph of the conic.

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