Question

Let E be the ellipse given by the equation x^2+5y^2=6. If m is any real number, find all tangent lines to E that pass through the point (m,0). Your solution should describe how you know that you have found all such lines.

The Ellipse E has a tangent line with positive slope that passes through the point (-6,0). Find the point of intersection of this line with the vertical line x=9.