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Q.
Find the centre and radius of circle $x^{2}+y^{2}-2 x + 4y=8$.
Conic Sections
Solution:
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 $\sqrt{13}$.