Prove that the locus of points from which the two tangents to E are perpendicular is the circle [math]x^2+y^2=a^2+b^2[/math].

I first created a slider for a and b. Then I constructed a circle using the equation [math]x^2+y^2=a^2+b^2[/math] then I constructed the eclipse using the equation [math]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/math]. I constructed a point on the circle and the tangent lines from the eclipse through A and the intersection of the tangent lines and c. I then constructed the angle between tangent 1, A, and tangent 2.