Finding points where perpendicular tangents to an ellipse meet

[kevinchhan]

Having trouble with this:

Given an ellipse (x^2/a^2) + (y^2/b^2) = , a!=b. Find the equation of the set of all points from which the two tangents to the curve are perpendicular.

I tried finding the slope of the equation then knowing that perpendicular line are the opposite reciprocal. But still clueless on how to put it together.

Thanks in advance

 

[HallsofIvy]

The points in question are not on the ellipse. Suppose $(x_0, y_0)$ is a point not on the ellipse. Then there are two lines tangent to the ellipse through $(x_0, y_0)$. What are there equations? What must be true if those two lines are perpendicular?