Given:

$\displaystyle

xy^{2} + 5x^{2} = 4y

$

Find the equation of the tangent line at x = 1

Say what?

Deriving the implicit function of y with respect to x yields:

$\displaystyle

\frac{dy}{dx} = \frac{5}{y-2}

$

but I'm completely stuck on how to find the equation of the tangent line from this (assuming I did this correctly).

This equation doesn't seem to be a function. I get multiple values of y for x equal 1.

Was I tricked?