Question

The parametric form of equation of the circle $x^2+y^2-6x+2y-28=0$ is

• A. $x=-3+\sqrt{38}cos\theta ,y=-1+\sqrt{38}sin\theta$
• B. $x\sqrt{28}cos\theta ,y=\sqrt{28}sin\theta$
• C. $x=-3-\sqrt{38}cos\theta ,y=1+\sqrt{38}sin\theta$
• D. $x=3+\sqrt{38}cos\theta ,y=-1+\sqrt{38}sin\theta$

Answer 1

Answer: (D)

$E{q}^n$ of circle is
$x^2+y^2-6x+2y-28=0$
$2g=-6\Rightarrow g=-3$ and $2f=2\Rightarrow f=1$
$c=-28$
$\therefore r=\sqrt{g^2+f^2-c}=\sqrt{9+1+28}$
$=\sqrt{38}$
centre $:=\left(-g,-f\right)=\left(3,-1\right)=\left(h,k\right)$
$\therefore x=h+r.cos\theta$, and $y=k+rsin\theta$
$\Rightarrow x=3+\sqrt{38}cos\theta ,y=-1+\sqrt{38}sin\theta$