Let O be the vertex of the parabola x 2 4 y and Q be an... | null (Mathematics)

JEE Mains 2026 21st January Shift 1

Mathematics

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:

5 x-y-3=0

4 x-5 y+6=0

x-2 y+3=0

5 x-4 y+3=0

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Explanation

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

\\

\mathrm{k}=\frac{2 \mathrm{t}^{2}}{5}=\frac{2}{5} \cdot\left(\frac{5 \mathrm{~h}}{4}\right)^{2}\\

8 \mathrm{k}=5 \mathrm{~h}^{2}\\

\Rightarrow 5 \mathrm{x}^{2}=8 \mathrm{y}\\

\mathrm{T}=\mathrm{S}_{1}\\

5\left(\mathrm{xx}_{1}\right)-4\left(\mathrm{y}+\mathrm{y}_{1}\right)=5 \mathrm{x}_{1}{ }^{2}-8 \mathrm{y}_{1}\\

5(\mathrm{x})-4(\mathrm{y}+2)=5-8.2\\

5 x-4 y+3=0

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