Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2: 3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1,2), is :
A. 5 x-4 y+3=0
Parabola x^2 = 4y, vertex O = (0, 0), Q = (2t, t^2) on parabola. P divides OQ in ratio 2:3: P = ( 4t 5 , 2t^2 5 ). Eliminating t: x^2 = 8y 5 (conic C with a = 2 5 ). For chord with midpoint (h, k): hx - 2ay = h^2 - 2ak. At (1, 2): x - 4y 5 = 1 - 8 5 = - 3 5 . 5x - 4y + 3 = 0.
Related: Mathematics — Parabola · All PYQ Banks