Let a line y = m x m 0 , intersect the parabola, y 2 = x , at a point P , other than the origin. Let the tangent to it a P , meet the x -axis at the point Q . If area Δ O P Q = 4 square unit, then m is equal to

Question

Let a line y = m x m > 0 , intersect the parabola, y 2 = x , at a point P , other than the origin. Let the tangent to it a P , meet the x -axis at the point Q . If area Δ O P Q = 4 square unit, then m is equal to,

MARKS App · Accepted Answer

Let the equation of tangent at P is 2 t y = x + t 2 So, Q - t 2 , 0 As given, area Δ O P Q = 4 square unit, so 1 2 0 0 1 t 2 t 1 - t 2 0 1 = ± 4 t 3 = ± 8 t = 2 t > 0 So, m = t t 2 = 1 2 .

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