Parabola x2=4y, vertex O = (0, 0), Q = (2t,t2) on parabola.
P divides OQ in ratio 2:3: P=(54t,52t2).
Eliminating t: x2=58y (conic C with a=52).
For chord with midpoint (h,k): hx−2ay=h2−2ak.
At (1,2): x−54y=1−58=−53.
5x−4y+3=0.
Let O be the vertex of the parabola x2=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 :
Held on 21 Jan 2026 · Verified 6 Jul 2026.
5x−4y+3=0
5x−y−3=0
4x−5y+6=0
x−2y+3=0
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