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Let a line y=mx (m>0) intersect the parabola, y2=x at a point P , other than the origin. Let the tangent to it at P meet the x -axis at the point Q . If area (ΔOPQ)=4sq . units, then m is equal to _________

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Detailed Solution

Equation of tangent at Pt2,t is 2ty=x+t2 ⇒Q=-t2,0∴ Area of ∆OPQ=12|001t2t1-t201∣=4⇒|t|3=8⇒t=±2⇒t=2⇒m=12

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Let a line y=mx (m>0) intersect the parabola, y2=x at a point P , other than the origin. Let the tangent to it at P meet the x -axis at the point Q . If area (ΔOPQ)=4sq . units, then m is equal to _________