Posted by Abi on Thursday, March 17, 2011 at 1:32am.
Find the slope of the tangent line to the ellipse x^2/36 + y^2/49 =1 at the point (x,y).
slope =_______
Are there any points where the slope is not defined? (Enter them as commaseparated orderedpairs, e.g., (1,3), (2,5). Enter none if there are no such points.)
slope is undefined at____
Please help..

Calculus  drwls, Thursday, March 17, 2011 at 2:52am
Use implicit differentiation, by differentiating each side of the equation with respect to x.
x/18 + (2y/49)*dy/dx = 0
dy/dx = (49/2)(x/18y)
= (49/36)(x/y)
The slope is undefined where y = 0, which is where x = +/ 6:
(6,0) and (6,0)