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Match the conditions/expression in Column I With statement in Column II. Normals at P,Q,R are drawn to `y^(2) = 4x` which intersect at (3,0). Then, `{:("column I","column II"),(A."Area of" Delta PQR,p.2),(B. "Radius of circumcircle of" Delta PQR,q.(5)/(2)),(C. "Centroid of" Delta PQR,r. ((5)/(2),0)),(D. "Circumcentre of" Delta PQR,s. ((2)/(3),0)):}` |
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Answer» Correct Answer - `A to p; B to q: C to s; D to r` since, equation of normal to the parabola `y^(2) = 4ax` is `y + xt = 2at + at^(3)` passes through (3,0) `implies 3t = 2t + t^(2)` `implies t = 0, 1 -1` `:. ` Coordinates of the normals are `P(1,2), Q(0,0) R(1,-2)` Thus, A. Area of `Delta PQR = (1)/(2) xx 1 xx 4 = 2` C. Centriod of `Delta PQR = ((2)/(3), 0)` Equation of circle passing through P,Q,R is (x - 1)(x -1) + (y - 2) (y + 2) + `lambda` (x - 1) = 0 `implies 1 - 4 - lambda = 0` `implies lambda = - 3` `:.` Required equation of circle is `x^(2) + y^(2) - 5x = 0` `:.` Centre `((5)/(2) , 0)` and radius `(5)/(2)`. |
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