The graph of $x^3 = 5xy + 2y^2$ is shown below. 

1. How many tangent lines exist at $x =-2$?

   Hint (a):

   How many coordinate points does this graph have at
   $x =-2$?

2. Find the equations of the tangent lines at $x =-2$.

   Hint 1(b):

   Write two tangent line equations in point-slope form.
   You already know the points.

   Hint 2(b):

   Use the derivative to find the corresponding slopes. You will have to use implicit differentiation.

   Hint 3(b):

   Because you used implicit differentiation, your derivative might have both $x$- and $y$-values.
   That means you will need $(x, y)$ coordinate points to evaluate.