JEE Main 6 Apr 2024 Shift 1 Solved Paper

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 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 ______.