Thread: Find an equation of the tangent line to the curve at a given point.

I know how to find the tangent line to the curve, but for some reason I can't simplify the following two equations into y=mx+b form so that I can take the derivative. If you can help me simplify them (and show me your steps) I'd really appreciate it. Thanks.

a) 2(x^2+y^2)^2=25(x^2-y^2)

b) x^2y^2=(y+1)^2(4-y^2)

Where did you learn that you can only differentiate linear functions?

Originally Posted by dptrimble

I know how to find the tangent line to the curve, but for some reason I can't simplify the following two equations into y=mx+b form so that I can take the derivative. If you can help me simplify them (and show me your steps) I'd really appreciate it. Thanks.

a) 2(x^2+y^2)^2=25(x^2-y^2)

b) x^2y^2=(y+1)^2(4-y^2)

you need to use implicit differentiation to find the derivative.

once you find the derivative, you evaluate it at a given point (x,y) to find the slope ... then y = mx+b comes into play.

Thanks