Find the slope of the tangent line to the ellipse x^2/4 + y2/16=1

Are there any points where the slope is not defined? (Enter them as semicolon-separated ordered-pairs, e.g., (1,3); (-2,5). Enter none if there are no such points.)
slope is undefined at

Question

Find the slope of the tangent line to the ellipse x^2/4    + y2/16=1

Are there any points where the slope is not defined? (Enter them as semicolon-separated ordered-pairs, e.g., (1,3); (-2,5). Enter none if there are no such points.) 
slope is undefined at

anonymous · Answer

I found the slope to be -32x/8y but not sure how to get the 2nd part.

zepdrix · Answer

|dw:1351901571062:dw|
Do you understand why the slope is undefined there? :D
Do you know how to find the coordinates of that point? There should be one more point like that also.