Question

If $x=acosec\theta$ and $y=bcot\theta$, then which of the following equations is true ?

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

Answer 1

The correct option is B

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

$x=acosec\theta \Rightarrow \frac{x}{a}=cosec\theta$.....(1)

$y=bcot\theta \Rightarrow \frac{y}{b}=cot\theta$.....(2)

Squaring the equations and subtracting (2) from (1) we get,

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=cose{c}^2\theta -co{t}^2\theta$

$\therefore \frac{x^2}{a^2}-\frac{y^2}{b^2}=\mathrm{1....}(1+co{t}^2\theta =cose{c}^2\theta )$