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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..

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1 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)

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