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Chapter 10: Q 10. (page 676)

True or False

To eliminate the xy-term from the equation x2-2xy+y2-2x+3y+5=0, rotate the axes through an angle 胃, where cot胃=B2-4AC.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Step 1. Given information

An equation isx2-2xy+y2-2x+3y+5=0.

02

Step 2. State whether the statement is true or false.

The angle 胃through which the axes are to be rotated is defined by the equation role="math" localid="1646725134009" cot2胃=A-CBin order to eliminate the xy-term from the equation of the conic.

The given statement is therefore not correct, hence the given statement is False.

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Most popular questions from this chapter

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.x2+3xy-2y2+3x+2y+5=0

In Problems 15鈥�18, the graph of a hyperbola is given. Match each graph to its equation.

Equations: Ax24-y2=1Bx2-y24=1Cy24-x2=1Dy2-x24=1

Graph:

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Center at (0,0); focus at (3,0); vertex at(1,0).

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.

x2-4xy+y2-3=0

Graph each function.

f(x)=9-9x2.
See all solutions

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