Let a conic \( C \) pass through the point \( (4,-2) \) and \( P(x,y) \), \( x \ge 3 \), by 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 \( 12d \) equals:
