Question

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 comma-separated ordered-pairs, e.g., (1,3), (-2,5). Enter none if there are no such points.)
slope is undefined at____

Please help..

Answer 1

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)