Let O be the vertex of the parabola x^2=4y 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…

Question

Let O be the vertex of the parabola x^2=4y 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 :

Accepted Answer

Correct answer: A. (a) Parabola x^2=4y, vertex O= (0 ,0 ) ,Q= (2t ,t^2 ) on parabola. P divides OQ in ratio 2:3: P= ( 4t5 , 2t^25 ). Eliminating t :x^2= 8y5 (conic C with a= 25 ). For chord with midpoint (h ,k ) : hx-2 ay=h^2-2 ak. At (1 ,2 ) :x- 4y5=1- 85=- 35. 5x-4y+3=0.

$Let O be the vertex of the parabola x^{2} = 4 y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2 : 3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is :$

Solution

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