The locus of the point, from which the chord of contact of tangents are to be drawn to the ellipse, touches the circle $x^2+y^2=c^2$ is.

Let the point from which the tangents are drawn be $(h, k)$.

So, the equation of the chord of contact from the point $(h, k)$ to the given ellipse is 

$\frac{hx}{a^2}+\frac{ky}{b^2}=1$     …(i)

It touches the circle $x^2+y^2=c^2$.

Therefore, the length of the perpendicular from the centre $(0, 0)$ to the chord of contact (i) is equal to the radius of the circle. 

Thus, $\left|\frac{0+0-1}{\sqrt{\frac{h^2}{a^4}+\frac{k^2}{b^4}}}\right|=c$

$\Rightarrow \frac{h^2}{a^4}+\frac{k^2}{b^4}=\frac{1}{c^2}$

Hence, the locus of $(h, k)$ is $\frac{x^2}{a^4}+\frac{y^2}{b^4}=\frac{1}{c^2}$