Given:

$4x^2+9y^2=36$

$\Rightarrow \frac{x^2}{9}+\frac{y^2}{4}=1$

Comparing with the standard form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, we get

$a^2=9 \& b^2=4$

Now, we know that the locus of two perpendicular tangents drawn to the ellipse is the director circle of the ellipse.

Now, equation of the director circle to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is given by $x^2+y^2=a^2+b^2$.

Therefore, required curve is 

$x^2+y^2=9+4$

or$x^2+y^2=13$.