Question

Find the centre and radius of the circle:
$\frac{1}{2}(x^2+y^2)+Xcos\theta +ysin\theta -4=0$

Answer 1

Given circle $\frac{(x^2+y^2)}{2}+xcos\theta +ysin\theta -4=0$

$\Rightarrow x^2+y^2+2xcos\theta +2ysin\theta -8=0$

center = $(-cos\theta ,-sin\theta )$

radius = $\sqrt{(-cos\theta {)}^2+(-sin\theta {)}^2+8}$

$=\sqrt{co{s}^2\theta +si{n}^2\theta +8}$

$=\sqrt{1+8}=\sqrt{9}=3$

$\therefore$ radius of circle = 3 units