The normals to the parabola y 2 = 4 ax at points Q and R meet the parabola again at P . If T is the intersection point of the tangents to the parabola at Q and R, then the locus of the centroid of △ T

Question

The normals to the parabola y 2 = 4 ax at points Q and R meet the parabola again at P . If T is the intersection point of the tangents to the parabola at Q and R, then the locus of the centroid of △ TQR , is

TestHub · Accepted Answer

Let Q = ( at 1 2 ​ , 2 at 1 ​ ) R = ( at 2 2 ​ , 2 at 2 ​ ) Normals at Q \& R meet on parabola Also T = ( at 1 ​ t 2 ​ , a ( t 1 ​ + t 2 ​ ) ) Let ( α , β ) be centroid of Δ QRT Then 3 α = a ( t 1 2 ​ + t 2 2 ​ + t 1 ​ t 2 ​ ) & β = a ( t 1 ​ + t 2 ​ ) Eliminate ( t 1 ​ + t 2 ​ )

Mathematics - Parabola Question with Solution | TestHub

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