Explanation

(d)
The locus of the point of intersection of the perpendicular tangents to ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,$ is a director circle and whose equation is given by
$x^{2} + y^{2} = a^{2} + b^{2}$
$\therefore$ Here, the equation of director circle is
$x^{2} + y^{2} = 9 + 4\ \Rightarrow \ x^{2} + \ y^{2} = 13\$