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)

Algebra ->  Graphs -> 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)       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
If x%5E2%2F4+%2B+y%5E2%2F10=+14, then after differentiating implicitly and simplifying, we get
x%2F2%2B%28y%28dy%2Fdx%29%29%2F5+=+0
Substituting the coordinates of (4,10) into the last equation, we get
4%2F2%2B%2810%28dy%2Fdx%29%29%2F5+=+0
==> 2%2B+2%28dy%2Fdx%29+=+0, or dy%2Fdx+=+-1.
Hence the equation of the tangent line to the ellipse at the point (4,10) is
y-10 = -(x-4), or
highlight%28x+%2B+y+=+14%29