Question

The curve described parametrically by $y=B\tan \theta$ and $x=A\sec \theta$ represents

• A. Ellipse
• B. Parabola
• C. Hyperbola
• D. Circle

Answer 1

The correct option is C Hyperbola

Eliminating the parameter $\theta$ using ${\sec }^2\theta -{\tan }^2\theta =1$
${\left(\frac{x}{A}\right)}^2-{\left(\frac{y}{B}\right)}^2=1\Rightarrow \frac{x^2}{A^2}-\frac{y^2}{B^2}=1$
Which is standard form of a hyperbola.