Compute the derivative of y using implicit differentiation

Question

Consider the curve given by z² - zy - y² = 1 Compute the derivative of y using implicit differentiation and compute the equation of the tangent line to the curve at (2,1).

Answer 1

In this problem, apparently y is a function of z.

Implicit differentiation: 2z-z(dy/dz)-y-2y(dy/dz)=0

Collect terms to find dy/dz=3/4 at (2,1)

Then the tangent line is 3/4 = (y-1)/(z-2)