Line passing through an Ellipse and a Point

[Figurelli]

Please Help! Line passing through an Ellipse and a Point

Homework Statement

Hi guys, I'm new to the forum and I could really use some help with this problem.

There is an ellipse with the equation: (X^2/4) + Y^2 = 1

There is a point on the graph (4,0)

Find an equation that passes through the line and the point...(must use the chain rule)

Homework Equations

(X^2/4) + Y^2 = 1

The Attempt at a Solution

I attempted to derive the slope of the circle: (DY/DX) = (-.5X)/(2Y)...
What do I do from here? Was that part even right? Thanks!

 

[Phrak]

The line y=0 passes through the point and the ellipse. I think you want a line that passes through the point (4,0) and is tangent to the ellipse, right? In which case there are two of them.

 

[Figurelli]

Yes, I suppose you could find either equation but the one in the picture shows the line with a negative slope...

 

[Phrak]

You need two equations for slope, or dy/dx. One is the slope of the upper half of an ellipse. The other is for a line that passes through the point (4,0).