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

$\frac{x}{a}+\frac{y}{b}=K.....................\left(i\right)$
Put $\left(i\right)$ in this
$\frac{x}{a}-\frac{y}{b}=\frac{1}{K}\Rightarrow \frac{x}{a}-\frac{y}{b}=\frac{1}{\frac{x}{a}+\frac{y}{b}}\Rightarrow (\frac{x}{a}-\frac{y}{b})(\frac{x}{a}+\frac{y}{b})=1\Rightarrow {\left(\frac{x}{a}\right)}^2-{\left(\frac{y}{b}\right)}^2=1$
Equation of hyperbola