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  • Locus of mid-point of chords of the parabola that pass through the po

Locus of mid-point of chords of the parabola \mathrm{y^{2}=4 a x} that pass through the point \mathrm{(3 a, a)} is

Option: 1

\mathrm{y^{2}+2 a x+a y-6 a^{2}=0}


Option: 2

\mathrm{y^{2}+2 a x-a y+6 a^{2}=0}


Option: 3

\mathrm{y^{2}-2 a x+a y+6 a^{2}=0}


Option: 4

\mathrm{y^{2}-2 a x-a y+6 a^{2}=0}


Answers (1)

Let the mid point of chord be \mathrm{P(h, k)} then it's equation is

\mathrm{T=S_{1}}
\mathrm{i.e., \quad y k-2 a(x+h)=k^{2}-4 a h}
It must pass through \mathrm{(3 a, a)}, hence
\mathrm{a k-2 a(3 a+h)=k^{2}-4 a h}
Thus locus of P is

\mathrm{y^{2}-2 a x-a y+6 a^{2}=0}

Posted by

Ramraj Saini

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