ParabolaHard

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:

Options

A.$5x - y - 3 = 0$
B.$4x - 5y + 6 = 0$
C.$5x - 4y + 3 = 0$

Solution

$h = \frac{4t}{5}$

$${k = \frac{2t^{2}}{5} = \frac{2}{5} \cdot \left( \frac{5\text{ }h}{4} \right)^{2} }{8k = 5{\text{ }h}^{2} }{\Rightarrow 5x^{2} = 8y }{T = S_{1} }{5\left( {xx}_{1} \right) - 4\left( y + y_{1} \right) = 5x_{1}\ ^{2} - 8y_{1} }{5(x) - 4(y + 2) = 5 - 8.2 }{5x - 4y + 3 = 0}$$

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