Question

Find the centre and radius of the circle $x^2+y^2-x+2y-3=0$.

Answer 1

given equation is $x^2+y^2-x+2y-3=0$

$\Rightarrow$ $(x^2-2\times \frac{1}{2}\times x+\frac{1}{4})+(y^2+2y+1)$

$\Rightarrow 3+\frac{1}{4}+1$

$\Rightarrow {(x-\frac{1}{2})}^2+{(y+1)}^2=\frac{17}{4}$

$\therefore$ the centre is $(\frac{1}{2},-1)$ and raius is $\frac{\sqrt{17}}{2}$