Question

The locus of the point of intersection of the lines $xcot\theta +ycosec\theta \text{=}2$ and $xcosec\theta +ycot\theta =6$ is

• A. a straight line
• B. circle
• C. a hyperbola
• D. an ellipse

Answer 1

Answer: (C)

Given equations are $x\cot \theta +y\text{cosec }\theta \text{=2}$ ...(i) and $\text{x cosec }\theta +y\cot \theta =6$ ...(ii) On squaring and subtracting Eq. (i) from Eq. (ii), we get
$x^2(\text{cose}{\text{c}}^2\theta -{\cot }^2\theta )+y^2({\cot }^2\theta -\text{cose}{\text{c}}^2\theta )$
$={(6)}^2-{(2)}^2$
$\Rightarrow$ $x^2-y^2=32$
It represents an equation of hyperbola.