SOLUTION: What is the equation of the line tangent to the parabola y^2=4x at point (4,4)?

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Question 1110828: What is the equation of the line tangent to the parabola y^2=4x at point (4,4)?
Answer by greenestamps(13208) About Me  (Show Source):
You can put this solution on YOUR website!


Use implicit differentiation to find an expression for the slope, dy/dx.

y%5E2+=+4x
2y%28dy%2Fdx%29+=+4
dy%2Fdx+=+4%2F%282y%29
dy%2Fdx+=+2%2Fy

At the point (4,4), the slope is
2%2F4+=+1%2F2

Now you have a point (4,4) and a slope 1/2.

Presumably if you are working on a problem like this you know how to find the equation of the line, given the slope and a point on the line.