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  • If is a variable, the locus of the point of intersection of the lines <img alt="\mathrm{\frac{x}{3}-\

If \mathrm{m} is a variable, the locus of the point of intersection of the lines \mathrm{\frac{x}{3}-\frac{y}{2}=m\: and \: \frac{x}{3}+\frac{y}{2}=\frac{1}{m}} is a/an

Option: 1

parabola


Option: 2

ellipse


Option: 3

 hyperbola


Option: 4

none of these


Answers (1)

best_answer

The required locus is obtained by eliminating the variable \mathrm{m} from the given equations of the lines. Then we have

\mathrm{\left(\frac{x}{3}-\frac{y}{2}\right)\left(\frac{x}{3}+\frac{y}{2}\right)=m\left(\frac{1}{m}\right) \Rightarrow \frac{x^{2}}{9}-\frac{y^{2}}{4}=1}

This is clearly a hyperbola.

Posted by

shivangi.bhatnagar

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