Question

Eliminate ${}^{\prime }{\theta }^{\prime }$ from the $x$ $=$ $a$ $\sec \theta$, $y$ $=$ $b$ $\tan \theta$

• A. $\frac{x^2}{a^2}-\frac{y^2}{b^2}$ $=$ 1
• B. $\frac{x^2}{a^2}+\frac{y^2}{b^2}$ $=$ 1
• C. $\frac{y^2}{b^2}-\frac{x^2}{a^2}$ $=$ 1
• D. $\frac{x^2}{b^2}+\frac{y^2}{b^2}$ $=$ 1

Answer 1

Answer: (A)

$\frac{x^2}{a^2}-\frac{y^2}{b^2}$ $=$ 1

$x=a\sec \theta ⟹\frac{x}{a}=\sec \theta$

$y=b\tan \theta ⟹\frac{y}{b}=\tan \theta$

$1+{\tan }^2\theta ={\sec }^2\theta$

$⟹1=-{\tan }^2\theta +{\sec }^2\theta$

$⟹\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$