SOLUTION: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given point. x^2/4 + y^2/10= 14, (4, 10)

Question 1022660: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given point.
x^2/4 + y^2/10= 14, (4, 10)

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
If , then after differentiating implicitly and simplifying, we get

Substituting the coordinates of (4,10) into the last equation, we get

==> , or .
Hence the equation of the tangent line to the ellipse at the point (4,10) is
y-10 = -(x-4), or

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