Question

Find the centre and radius of circle $x^2+y^2-2x+4y=8$.

• A. $\left(1,2\right),\sqrt{13}$
• B. $\left(1,-2\right),\sqrt{13}$
• C. $\left(-1,-2\right),\sqrt{13}$
• D. $\left(2,-1\right),\sqrt{13}$

Answer 1

Answer: (B)

We write the given equation in the form
$\left(x^2-2x\right)+\left(y^2+4y\right)=8$
Now, completing the squares, we get
$\left(x^2-2x+1\right)+\left(y^2+4y+4\right)=8+1+4$
or ${\left(x-1\right)}^2+{\left(y+2\right)}^2=13$
Comparing it with the standard form of the equation of the circle, we see that the centre of the circle is $\left(1,-2\right)$ and radius is $\sqrt{13}$.