vertical lines?

Question

How do you find the coordinates of the points on the curve where the tangent lines are vertical given that the curve is:
x^2 - xy + y^2 = 9.

I already found the derivative of the formula, I just don't know how to find the vertical lines. Please show your work

Answer 1

The easiest way is to use implicit differentiation to find the derivitive of x with respect to y (dx/dy). There will be a vertical tangent line when this derivitive is zero.

If instead you found the derivitive of y with respet to x (dy/dx) you need to examine the points where dy/dx is undefined. Use these undefined points to show that the limit approaches infinity or negative infinity from both sides at that point.