QJEEM24Mac7f1: JEE Main 2024 Mathematics - Class 11 JEEM24Mac7f1 Solution: Let a conic C pass through the point ( 4 , − 2 ) and P ( x , y…

Let a conic $$C$$ pass through the point $$(4,-2)$$ and $$P(x,y),x\ge 3$$, 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 ________.