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Locus of the mid-point of chords of the ellipse \mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}=1}  that are parallel to the line \mathrm{y=2 x+c} , is

Option: 1

\mathrm{2 b^2 y-a^2 x=0}


Option: 2

\mathrm{2 a^2 y-b^2 x=0}


Option: 3

\mathrm{2 b^2 y+a^2 x=0}


Option: 4

\mathrm{2 a^2 y+b^2 x=0}


Answers (1)

best_answer

Let the mid-point of chord be P(h, k).

Equation of this chord will be T=S_1

\mathrm{\text { i.e. } \frac{x h}{a^2}+\frac{y k}{b^2}=\frac{h^2}{a^2}+\frac{k^2}{b^2} \Rightarrow \frac{h}{2 a^2}=-\frac{k}{b^2} \Rightarrow k=-\frac{b^2}{2 a^2} \cdot h}

\mathrm{\text { Thus the required locus is } y=-\frac{b^2}{2 a^2} x}

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Ritika Harsh

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