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  • The locus of the middle points of chords of hyperbola <img alt="\mathrm{3 x^2-2 y^2+4 x-6 y=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20x%5E2-2%20y%5E2&plus;4%20x-6

The locus of the middle points of chords of hyperbola \mathrm{3 x^2-2 y^2+4 x-6 y=0} parallel to \mathrm{y=2 x} is 

Option: 1

\mathrm{3 x-4 y=4}


Option: 2

\mathrm{3 x-4 y+4=0}


Option: 3

\mathrm{4 x-4 y=3}


Option: 4

\mathrm{3 x-4 y=2}


Answers (1)

best_answer

Let the mid point be (h, k). Equation of a chord whose mid point is \mathrm{(h, k)} would be \mathrm{\mathrm{T}=\mathrm{S}_1}

\mathrm{\text { or } \quad 3 \mathrm{xh}-2 \mathrm{yk}+2(\mathrm{x}+\mathrm{h})-3(\mathrm{y}+\mathrm{k})=3 \mathrm{~h}^2-2 \mathrm{k}^2+4 \mathrm{~h}-6 \mathrm{k}}
\mathrm{\Rightarrow \quad x(3 h+2)-y(2 k+3)-(2 h+3 k)-3 h^2+2 k^2=0}
Its slope is\mathrm{}\mathrm{\frac{3 h+2}{2 k+3}=2} (given)
\mathrm{\Rightarrow \quad 3 h=4 k+4}
Required locus is\mathrm{3 x-4 y=4}
Hence (a) is the correct answer.

 

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Sayak

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