Implicit Differentiation Tangent lines

[htoor9]

Homework Statement

Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line.

Homework Equations

dy/dx dx/dy or something not sure.

The Attempt at a Solution

Well I know that a horizontal tangent line would mean the slope is zero...but what exactly do I do?

 

[Mark44]

Homework Statement

Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line.

Homework Equations

dy/dx dx/dy or something not sure.

The Attempt at a Solution

Well I know that a horizontal tangent line would mean the slope is zero...but what exactly do I do?

The easiest thing to do is to use implicit differentiation to get dy/dx, then set it to zero. Since the graph is an ellipse, there should be two points where dy/dx = 0.