How do I get the derivative of this curve

Hi,

I have this equation: xy+y^2=a

Where a is not equal to 1

I need the derivative as this curve intersects y=1.

Where do I start and how do I do this?

first evaluate x in terms of a at y = 1 by setting y = 1, we get
x + 1 = a, x = a-1

now we take the derivative of the implicit curve
y + x(dy/dx) + 2y(dy/dx) = 0
(x+2y)(dy/dx) = -y
(dy/dx) = -y/(x + 2y)
subbing in y=1, x = a-1
(dy/dx) = -1/(a + 1) which is your answer.

Are you sure it isn't a is not equal to -1? because that seems more sensible in this situation