Question

Eliminate $\theta$, if $r=y\text{cosec}\theta$ and $x=y\cot \theta$.

Answer 1

From the given values we get,

$\text{cosec}\theta =\frac{r}{y}$, $\cot \theta =\frac{x}{y}$......(1)

We know that $\text{cosec}{}^2\theta +{\cot }^2\theta =1$

so we get from (1) ,

${\left(\frac{r}{y}\right)}^2+{\left(\frac{x}{y}\right)}^2=1$