The locus of the point of intersection of tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ which meet at right angle, is

The locus of the point of intersection of perpendicular tangents to an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is its director circle $x^2+y^2=a^2+b^2.$