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

Answer: (D)

a hyperbola

Given $x=a(t+\frac{1}{t})..\left(1\right)$ and $y=b(t-\frac{1}{t})..\left(2\right)$
Using (1) and (2)
$\frac{x}{a}+\frac{y}{b}=2t$ and $\frac{x}{a}-\frac{y}{b}=\frac{2}{t}$
Eliminating parameter $t$ we get
$\frac{x^2}{4a^2}-\frac{y^2}{4b^2}=1$
Clearly, this is a hyperbola,
Hence, option 'D' is correct..