Explanation

(b)
Any point on the ellipse is $P(3\cos{\theta,\ {2\ sin}{\theta)}}$
Equation of the tangent at $P$ is
$\frac{x}{3}\cos\theta + \frac{y}{2}\sin\theta = 1$
Which meets the tangents $x = 3$ and $y = - 3$ at the extremities of the major axis at $T\left( 3,\ \frac{2\left( 1 - \cos\theta \right)}{\sin\theta} \right)$ and $T^{'}\left( - 3,\ \frac{2\left( 1 + \cos\theta \right)}{\sin\theta} \right)$
Equation of circle on $TT'$ as diameter is
$(x - 3)(x + 3) + \left( y - \frac{2\left( 1 - \cos\theta \right)}{\sin\theta} \right)\left( y - \frac{2\left( 1 + \cos\theta \right)}{\sin\theta} \right) = 0$
$\Rightarrow x^{2} + y^{2} - \frac{4}{\sin\theta}y - 5 = 0$
Which passes through $(\sqrt{5},\ 0)$