Let a conic C pass through the point (4,-2) and P(x, y), x ≥ 3, be any point on C. Let the slope of the line touching the conic C only at a single…

Let a conic $\displaystyle C$ pass through the point $\displaystyle (4,-2)$ and $\displaystyle P(x, y), x \geq 3$, be any point on $\displaystyle C$. Let the slope of the line touching the conic $\displaystyle C$ only at a single point $\displaystyle P$ be half the slope of the line joining the points $\displaystyle P$ and $\displaystyle (3,-5)$. If the focal distance of the point $\displaystyle ( 7,1 )$ on $\displaystyle C$ is $\displaystyle d$, then $\displaystyle 12 d$ equals $\displaystyle \_\_\_\_$.