SOLUTION: Let x^2 + y^2 = 10y. First find dy/dx by implicit differentiation, simplifying the answer where reasonable. Then find an equation of the line L tangent to the graph of the g

Algebra ->  Finance -> SOLUTION: Let x^2 + y^2 = 10y. First find dy/dx by implicit differentiation, simplifying the answer where reasonable. Then find an equation of the line L tangent to the graph of the g      Log On


   

Question 1008865: Let x^2 + y^2 = 10y.
First find
dy/dx
by implicit differentiation, simplifying the answer where reasonable. Then find an equation of the line L tangent to the graph of the given equation at the point (3, 1).
I got te answer x/(5-y) for dy/dx but not sure how to find the line L tangent at 3,1
please explain.
Thnk you
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2=10y

2x%2B2y%2Aexpr%28%28dy%29%2F%28dx%29%29=10expr%28%28dy%29%2F%28dx%29%29

Divide through by 2

x%2By%2Aexpr%28%28dy%29%2F%28dx%29%29=5expr%28%28dy%29%2F%28dx%29%29

y%2Aexpr%28%28dy%29%2F%28dx%29%29-5expr%28%28dy%29%2F%28dx%29%29=-x

expr%28%28dy%29%2F%28dx%29%29%28y-5%29=-x

expr%28%28dy%29%2F%28dx%29%29=-x%2F%28y-5%29

expr%28%28dy%29%2F%28dx%29%29=-x%2F%28-5%2By%29

expr%28%28dy%29%2F%28dx%29%29=-x%2F%28-%285-y%29%29

expr%28%28dy%29%2F%28dx%29%29=x%2F%285-y%29

Yes you were right about the derivative.

The derivative is a formula for the slope of the 
tangent line at the point (x,y).

So the slope m of the tangent line at (3,1) is found by
substituting (x,y) = (3,1) in the derivative:

m=3%2F%285-1%29

m=3%2F4

Then use the point-slope formula for a line

y-y%5B1%5D=m%28x-x%5B1%5D%29 where (x1, y1) = (3,1)

y-1+=+expr%283%2F4%29%28x-3%29

y-1+=+expr%283%2F4%29x-9%2F4

y+=+expr%283%2F4%29x-9%2F4%2B1

y+=+expr%283%2F4%29x-9%2F4%2B4%2F4

y+=+expr%283%2F4%29x-5%2F4



Edwin