Parabola

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