Conic Sections · Parabola chord with given midpoint

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:

We corrected a printing error in the original paper

Source labels the options “(1), (2), (4), (4)”; the third option ( $x - 2y + 3 = 0$ ) is printed as “(4)”, the key (4) is the last option.

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