Let O be the vertex and Q be any point on the parabola, x 2 = 8 y . If the point P divides the line segment O Q internally in the ratio 1 : 3 , then the locus of P is

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General point on x 2 = 8 y is Q 4 t , 2 t 2 Let P h , k divide O Q in ratio 1 : 3 h , k = 1 4 t + 3 0 1 + 3 , 1 2 t 2 + 3 0 1 + 3 h , k = t , 2 t 2 4 h = t & k = t 2 2 k = h 2 2 ⇒ x 2 = 2 y is the required locus.

Mathematics - Parabola Question with Solution | TestHub

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