Question:
Find the coordinates of those points on the curve given by the equation:
$\ x^2-0.25xy+y^2=16 $
at which the tangent line has slope 1.
Implicitly derived:$\ \frac{(-2x+0.25y)}{(2y-0.25x)} $
The book talked something about solving for y (from the original equation):
$\ \pm \sqrt{-x^2+0.25xy+16}$
then substituting it back into the implicitly derived equation and solving, but I am not sure that is going to work or else it is going to be very cumbersome. Anyone know how to solve this, perhaps in a simpler (possibly more correct) fashion? Thanks!
P.S. I spent 30mins figuring out the mathTex stuff so it looks pretty, it was the least I could do I suppose? Only for all you picky math geniuses who are going to help me! :)