Question

Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form.

61x^2 - 22xy + 61y^2 - 1800 = 0

Answer 1

Solve this one in the same way as I showed in your previous question. Replace x=u-v and y=u+v. After you plug these numbers in, you will get an equation with just a u^2 term, a v^2 term, and a constant term. Put it in the form \[\frac{u^2}{a}+\frac{v^2}{b}=1\] and you are done.

Answer 2

\[\frac{u^2}{a^2}+\frac{v^2}{b^2}=1\]
equivalently
\[(\frac{u}{a})^2+(\frac{v}{b})^2=1\]
lets you work out the foci\[c^2 = |a^2-b^2|\]
more easily