Question

Equation of circle whose parametric equations are $x=5-5\sin t$ and $y=4+5\cos t$ is

• A. $(x+5{)}^2+(y-4{)}^2=25$
• B. $(x-5{)}^2+(y-4{)}^2=25$
• C. $(x-5{)}^2+(y+4{)}^2=25$
• D. $(x+5{)}^2+(y+4{)}^2=25$

Answer 1

The correct option is B $(x-5{)}^2+(y-4{)}^2=25$

Given $x=5-5\sin t,y=4+5\cos t$
$\Rightarrow x=5+5\cos (\frac{\pi }{2}+t),y=4+5\sin (\frac{\pi }{2}+t)$
$\Rightarrow (x-5{)}^2+(y-4{)}^2=5^2{\cos }^2(\frac{\pi }{2}+t)+5^2{\sin }^2(\frac{\pi }{2}+t)$
$\Rightarrow (x-5{)}^2+(y-4{)}^2=25$