Consider the parabola `y^(2)=4x`, let P and Q be two points `(4,-4)` and `(9,6)` on the parabola. Let R be a moving point on the arc of the parabola whose x-coordinate is between P and Q. If the maximum area of triangle PQR is K, then `(4K)^(1//3)` is equal to

Options

A. 1
B. 2
C. 5
D. 7

Answer

B

Explanation

Case 1 : Concurrency `rarr|(1,-2,-6),(3,1,-4),(lambda,4,lambda^(2))|=0 " "implies(lambda^(2)+16)+2(3lambda^(2)+4lambda)-6(12-lambda)=0`
`implies7lambda^(2)+14lambda-56=0implieslambda^(2)+2lambda-8=0implieslambda=-4,2`
Case 2 : `L_(1)||L_(3)implies(1)/(2)=-(lambda)/(4)=lambda=-2`
`L_(2)||L_(3)implies-3=-(lambda)/(4)implieslambda=12`