Question

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

(a) an ellipse

(b) a circle

(c) a hyperbola

(d) a parabola

Answer 1

SOLUTION — Multiplying given lines, we get

$\begin{array}{c}\left(\frac{x}{a}-\frac{y}{b}\right)\left(\frac{x}{a}+\frac{y}{b}\right)=m \cdot \frac{1}{m} \\\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\end{array}$

Which is the required equation of hyperbola

So, The correct option of this question will be (C).