Question

Eliminate $\theta$ from the equations, $x=2\cos \theta$ and $y=-2\sin \theta$

• A. $x^2-y^2=4$
• B. $x^2-y^2=2$
• C. $x^2+y^2=4$
• D. $x^2+y^2=2$

Answer 1

Answer: (C)

$x^2+y^2=4$

Given, $x=2cos\theta$ and $y=-2sin\theta$
Squaring them we get
$x^2=4co{s}^2\theta$ and $y^2=4si{n}^2\theta$
Adding them we get
$x^2+y^2=4co{s}^2\theta +4si{n}^2\theta$
$=>x^2+y^2=4(co{s}^2\theta +si{n}^2\theta )$
$=>x^2+y^2=4$ as $(co{s}^2\theta +si{n}^2\theta )=1$