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  • Find the locus of mid point of chords of the parabola that pass through the p

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

Option: 1

\mathrm{x^2-2 a y-a x+6 a^3=0}
 


Option: 2

\mathrm{y^2-2 a y-a x-6 a^2=0}
 


Option: 3

\mathrm{y^2-a y-2 a x+6 a^2=0}
 


Option: 4

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


Answers (1)

best_answer

Let the mid-point of chord be \mathrm{P(h, k)}, then its equation is \mathrm{ y k-2 a(x+h)=k^2-4 a h.}
As given it must passes through \mathrm{ (3 a, a).}
\mathrm{ \therefore \quad a k-2 a(3 a+h)=k^2-4 a h \text {. } }
Thus locus of \mathrm{ ' P ' \: is,\: \: y^2-2 a x-a y+6 a^2=0. }

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