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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

(a) What is the discriminant of the equation in 6 ( b ) ? How can you use the discriminant to determine the type of conic that equation represents.

(b) Use the discriminant to identify the equation in 6 ( c ) .

6 . (a) Suppose that the x and y axes are rotated through an acute angle ϕ to produce the X and Y axes. What are the equations that relates the coordinates ( x , y ) and ( X , Y ) of a point in a x y plane and X Y plane, respectively.

(b) In the equations below, how do you eliminate the x y term?

A x 2 + C y 2 + D x + E y + F = 0

(c) Use a rotation of axes to eliminate the x y term in the equation

25 x 2 14 x y + 25 y 2 = 288

Graph the equation.

To determine

(a)

To explain:

The discriminant of the equation in 6(b) and the usage of discriminant to determine the type of conic that equation represents.

Explanation

Given:

The equation from 6(b) is,

Ax2+Cy2+Dx+Ey+F=0(1)

Approach:

The general equation of discriminant of a conic is B24AC.

The graph is

1

To determine

(b)

To find:

The representation of equation in 6(c) with the help of discriminant.

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Chapter 12 Solutions

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