Question

Write the equation in terms of a rotated x'y'-system using θ, the angle of rotation. Write the equation involving x' and y' in standard form.

Answer 1

Hmm I dont' really remember how to rotate axes.
My book is giving me these formulas though:\[\Large x=x' \cos \theta-y' \sin \theta\]\[\Large y=x' \sin \theta+y' \cos \theta\]

Answer 2

Where theta is the angle of rotation.

So if we plug them in,\[\large xy=-16 \quad\to\quad \left(x'\frac{1}{\sqrt2}-y'\frac{1}{\sqrt2}\right)\left(x'\frac{1}{\sqrt2}+y'\frac{1}{\sqrt2}\right)=-16\]

Answer 3

From there it just requires a bit of simplification :o

Answer 4

That is where I am stuck :/

Answer 5

Let's factor the fraction out of each set of brackets.\[\Large \frac{1}{\sqrt2}\cdot\left(x'-y'\right)\frac{1}{\sqrt2}\cdot\left(x'+y'\right)=-16\]

Answer 6

So we have:\[\Large (x'-y')(x'+y')=-32\]

Answer 7

That was really helpful. Thank you very much. I've been trying to get help with this for 3 days.

Answer 8

ah that sucks :c