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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

15-28 Graphing a Rotated Conic (a) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use rotation of axes to eliminate the x y term. (c) Sketch the graph.

9 x 2 24 x y + 16 y 2 = 100 ( x y 1 )

To determine

(a)

Whether the graph of the equation is a parabola, an ellipse, or a hyperbola using a discriminant.

Explanation

Given:

The equation of the conic section is,

9x224xy+16y2=100(xy1)

Approach:

The graph of the equation

Ax2+Bxy+Cy2+Dx+Ey+F=0

is either a conic or a degenerate conic. In the non-degenerate cases the graph is

• A parabola if B24AC=0.

• An ellipse if B24AC<0.

• A hyperbola if B24AC>0.

the quantity B24AC is called the discriminant of the equation.

Calculation:

Consider the equation.

9x224xy+16y2=100(xy1)9x224xy+16y2100x+100y+100=0

Compare the equation with the equation of a conic section

To determine

(b)

To use:

Rotation of axes to eliminate the xy term.

To determine

(c)

To sketch:

The graph for the equation 25Y220X+140Y+100=0.

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