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From the point (15, 12) three normals are drawn to the parabola y2 = 4x, then centroid of triangle formed by three co-normal points is
(C)
Sol. Let the equation of any normal be y = – tx + 2t + t3
Since it passes through the points (15, 12)
\ 12 = –15t + 2t + t3 i.e. t3 – 13t – 12 = 0
\ t = –1, –3/4
\ The points are (1, –2), (9 – 6), (16, 8) \ Centroid is (26/3,0)
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