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JEE Main20246 Apr 2024Morning ShiftMathematicsParabolaActual

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 12 d equals ______

Correct answer

0

Step-by-step solution

P(x, y) & x 3 Slope of line at P(x, y) will be d y d x = 1 2 ( y+5 x-3 ) aligned & 2 d y (y+5) = 1 (x-3) d x & 2 (y+5)= (x-3)+C aligned Passes through (4,-2) aligned & 2 (3)= (1)+C & C=2 (3) & 2 (y+5)= (x-3)+2 (3) & 2 ( ( y+5 3 ) )= (x-3) & ( y+5 3 )^2=(x-3) aligned (y+5)^2=9(x-3) Parabola gathered 4 a=9 a= 9 4 gathered aligned & d= ( 7 4 )^2+6^2 & d= 625 4 & d= 25 4 & 12 d=75 aligned

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