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Locus of the point of intersection of straight lines $\frac{x}{a}-\frac{y}{b}=m$ and $\frac{x}{a}+\frac{y}{b}=\frac{1}{m}$ is
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The correct answer is:
A hyperbola
$\begin{aligned}
& \frac{x}{a}-\frac{y}{b}=m ....(i) \\
& \frac{x}{a}+\frac{y}{b}=\frac{1}{m} ....(ii)
\end{aligned}$
Multiplying equation (i) and (ii),
$\begin{aligned}
& \left(\frac{x}{a}-\frac{y}{b}\right)\left(\frac{x}{a}+\frac{y}{b}\right)=m \cdot \frac{1}{m} \\
& \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \text { which is, which is the equation of hyperbola. }
\end{aligned}$
& \frac{x}{a}-\frac{y}{b}=m ....(i) \\
& \frac{x}{a}+\frac{y}{b}=\frac{1}{m} ....(ii)
\end{aligned}$
Multiplying equation (i) and (ii),
$\begin{aligned}
& \left(\frac{x}{a}-\frac{y}{b}\right)\left(\frac{x}{a}+\frac{y}{b}\right)=m \cdot \frac{1}{m} \\
& \frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \text { which is, which is the equation of hyperbola. }
\end{aligned}$
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