Chapter 10: Q 10. (page 676)

True or False
To eliminate the $x y -$ term from the equation $x^{2} - 2 x y + y^{2} - 2 x + 3 y + 5 = 0$ , rotate the axes through an angle $θ$ , where $\cot θ = B^{2} - 4 A C$ .

Short Answer

Expert verified

The given statement is false.

Step by step solution

Step 1. Given information

An equation is $x^{2} - 2 x y + y^{2} - 2 x + 3 y + 5 = 0$ .

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

The angle $θ$ through which the axes are to be rotated is defined by the equation role="math" localid="1646725134009" $\cot (2 θ) = \frac{A - C}{B}$ in order to eliminate the $x y -$ term from the equation of the conic.

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

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True or False
To eliminate the $x y -$ term from the equation $x^{2} - 2 x y + y^{2} - 2 x + 3 y + 5 = 0$ , rotate the axes through an angle $θ$ , where $\cot θ = B^{2} - 4 A C$ .

Short Answer

Step by step solution

Step 1. Given information

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

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True or FalseTo eliminate the xy-term from the equation x2-2xy+y2-2x+3y+5=0, rotate the axes through an angle θ, where cotθ=B2-4AC.

Short Answer

Step by step solution

Step 1. Given information

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

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Study anywhere. Anytime. Across all devices.

True or False
To eliminate the $x y -$ term from the equation $x^{2} - 2 x y + y^{2} - 2 x + 3 y + 5 = 0$ , rotate the axes through an angle $θ$ , where $\cot θ = B^{2} - 4 A C$ .