The circle x² + y² - 4x - 6y + 9 = 0 is crossed at right angles by the circle x² + y² + 2x + ky - 4…

Step 1. The constants. For the first circle $g_1 = -2$, $f_1 = -3$ and $c_1 = 9$. For the second $g_2 = 1$, $f_2 = \dfrac{k}{2}$ and $c_2 = -4$.

Step 2. The condition. $2(-2)(1) + 2(-3)\dfrac{k}{2} = 9 - 4$, so $-4 - 3k = 5$ and $k = -3$.

Step 3. The distance. The centres are $(2, 3)$ and $(-1, 1.5)$. So $d^2 = 3^2 + 1.5^2 = 11.25$.