Implicit Differentiation of x2 + y2 = 9 at (0, 3) and

[grodrig]

Hi I would be very appreciative if someone could help me with this problem.
I was given the equation x2 + y2 = 9 and the points (0,3) and (2, sqrt(5) ). From there I am to find the tangent line and the normal (perpendicular) line. The topic we are currently discussing is implicit differentiation.

So far I assume that I must take the first derivitive:
2x + 2yy' = 0

then

2yy'/2y=-2x/2y

then

y' = -x/y

Am I correct in my assumptions? Please help me with this problem and how to find the equations for the tangent line and normal line in reference to the given information.

 

[stapel]

Do you mean your function to be "x^2 + y^2 = 9", or something else? What are you supposed to do with the points? Are you finding the normal at one point and the tangent at another? Or finding the normal that passes through the tangent at the other? The intersection of the two? Or something else?

Thank you.

Eliz.