Question

The standard equation of the circle whose parametric equation 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 $x=5-5\sin t,y=4+5\cos t$
$\frac{x-5}{5}=-\sin t,\cdots \left(1\right)\frac{y-4}{5}=\cos t\cdots \left(2\right)$
Squaring and adding equations $\left(1\right)$ and $\left(2\right)$
$\Rightarrow \frac{(x-5{)}^2}{5^2}+\frac{(y-4{)}^2}{5^2}=(-\sin t{)}^2+(\cos t{)}^2\therefore (x-5{)}^2+(y-4{)}^2=25$