Question

True or False

To eliminate the $xy-$term from the equation $x^2-2xy+y^2-2x+3y+5=0$, rotate the axes through an angle $\theta$, where $\cot \theta =B^2-4AC$.

Short answer

The given statement is false.

Step-by-step solution

Step 1. Given information

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

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

The angle $\theta$through which the axes are to be rotated is defined by the equation role="math" localid="1646725134009" $\cot \left(2\theta \right)=\frac{A-C}{B}$in 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.