Rotation of Axes · Exercise 1

Using rotation of axes formulas:

Find a new representation of the given equation after rotating through the given angle. Use the steps outlined to assist you in your work.
$4x^2–xy+4y^2-2=0,\theta =45o$

$$\begin{array}{c}\text{Find x and y using the rotation of axes formulas, substitute θ=45º.}\\ \text{Substitute the expressions for x and y into the given equation and simplify.}\\ \text{Write the equations with x′ and y′ in standard form.}\end{array}$$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §12.4 Rotation of Axes · Exercise 1