Question

The locus of the point of intersection of the straight lines $\frac{x}{a}+\frac{y}{b}=k$ and $\frac{x}{a}-\frac{y}{b}=\frac{1}{k}$, where $k$ is a non-zero real variable, is given by

• A. A straight line
• B. An ellipse
• C. A parabola
• D. A hyperbola

Answer 1

The correct option is D A hyperbola

We have, $\frac{x}{a}+\frac{y}{b}=k$ and $\frac{x}{a}-\frac{y}{b}=\frac{1}{k}$

Since $k$ is a parameter here, so to get the locus of point of intersection of

above two lines , we will need to eliminate $k$

So multiply both the equations,

$(\frac{x}{a}+\frac{y}{b})(\frac{x}{a}-\frac{y}{b})=k\cdot \frac{1}{k}=1$

$\Rightarrow \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, which is clearly a hyperbola equation