Question

Cartesian equations of a circle whose parametric equation are $x=-7+4\cos q$, $y=3+4\sin q$ is

• A. ${(x+7)}^2+{(y-3)}^2=16$
• B. ${(x-7)}^2+{(y-3)}^2=16$
• C. ${(x-7)}^2+{(y-3)}^2=12$
• D. ${(x+7)}^2+{(y+3)}^2=16$

Answer 1

The correct option is A ${(x+7)}^2+{(y-3)}^2=16$

We have,

$x=-7+4\cos q$

$y=3+4\sin q$

Now,

$x+7=4\cos q......\left(1\right)$

$y-3=4\sin q......\left(2\right)$

On squaring both side and adding we get,

${(x+7)}^2+{(y-3)}^2=16{\sin }^{2}q+16{\cos }^{2}q$

$\Rightarrow {(x+7)}^2+{(y-3)}^2=16({\sin }^{2}q+{\cos }^{2}q)$

$\Rightarrow {(x+7)}^2+{(y-3)}^2=16$

Hence, this is the answer.