Question

If t is a parameter, then $x=a(t+\frac{1}{t}),y=b(t-\frac{1}{t})$ represents

• A. An ellipse
• B. A circle
• C. A pair of straight lines
• D. A hyperbola

Answer 1

The correct option is D A hyperbola

Since, $x=a(t+\frac{1}{t})$ and $y=b(t-\frac{1}{t})$
$\therefore \frac{x^2}{a^2}-\frac{y^2}{b^2}={(t+\frac{1}{t})}^2-{(t-\frac{1}{t})}^2$
$=t^2+\frac{1}{t^2}+2-t^2-\frac{1}{t^2}+2$
$4$
$\Rightarrow \frac{x^2}{{4a}^2}-\frac{y^2}{{4b}^2}=1$
Thus, the given equation represents a hyperbola.