### Home > CALC > Chapter 6 > Lesson 6.4.1 > Problem 6-131

6-131.

The graph of

*x*^{3}= 5*xy*+ 2*y*^{2}is shown below. Homework Help ✎

How many tangent lines exist at

*x*=*−*2?Find the equations of the tangent lines at

*x*= −2.

How many coordinate points does this graph have at

*x* = −2?

Write two tangent line equations in point-slope form.

You already know the points.

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

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.

Use the eTool below to visualize the problem.

Click the link at right for the full version of the eTool: Calc 6-131 HW eTool