Robert J. answered • 11/25/12

Certified High School AP Calculus and Physics Teacher

Differentiate implicitly with respect to x,

8x + 2yy' - 8 + 4y' = 0

Solve for y',

y' = 4(1-x)/(y+2)

As y-->-2, y'-->+/-oo. So, the graph has a vertical tangent line.

Plug in y = -2 in the original equation to solve for x,

4x^{2} + 4 - 8x - 8 + 4 = 0

4x(x-2) = 0

x = 0, 2 <==Answer

Lana M.

thank you. perfect!

11/25/12