Explanation

(b)
The triangle is isosceles and therefore the median through $C$ is the bisector of $\angle C$. The equation of the angle bisector can be taken as $y = - x$and $l = ( - a,\ a)$, where $a$ is positive
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Equation of $AC$ is $y - 0 = - 7(x + 6)$ or $7x + y + 42 = 0$ and equation of $AB$ is $x - y + 6 = 0$
The length of the perpendicular from $l$ to $AB$ and $AC$ are equal
$\therefore\ \left| \frac{- 7a + a + 42}{\sqrt{50}} \right| = \left| \frac{- a - a + 6}{\sqrt{2}} \right|$
Giving the positive value $a = \frac{9}{2}$
$\therefore$ Centre is $\left( - \frac{9}{2},\frac{9}{2} \right)$ and radius $= \frac{3}{\sqrt{2}}$
The equation of the circle is
$\left( x + \frac{9}{2} \right)^{2}\left( y - \frac{9}{2} \right)^{2} = \frac{9}{2}$
$\Rightarrow x^{2} + y^{2} + 9x - 9y + 36 = 0$