Are there any points where the slope is not defined for problem 𝑥^2/36 + 𝑦^2/16 =1 ?

Question

Find the slope of the tangent line to the ellipse at 𝑥^2/36+𝑦^2/16=1 the point (x,y).

slope = -(2x/36)/(2y/16)

Are there any points where the slope is not defined? (Enter them as comma-separated ordered-pairs, e.g., (1,3), (-2,5).)

slope is undefined at points =

Answer 1

To get slope we use implicit differentiation: x/18 + y'y/8 = 0, from here y' = - 4x(9y).

So slpe is not defined if y = 0. We have y = 0, then x²/36 = 1; x = ± 6.

We get 2 point-vertices of ellypse: ( -6, 0) and (6, 0)