Question

Find the centre and radius of each of the following circles:

x² + y² − 4x + 6y = 5

Answer 1

Let (h, k) be the centre of a circle with radius a.
Thus, its equation will be

\[\left( x - h \right)^2 + \left( y - k \right)^2 = a^2\]

Given:

\[x^2 + y^2 - 4x + 6y = 5\]

The given equation can be rewritten as follows:

\[\left( x - 2 \right)^2 + \left( y + 3 \right)^2 - 4 - 9 = 5\]

\[\Rightarrow \left( x - 2 \right)^2 + \left( y + 3 \right)^2 = 18\]

Thus, the centre is (2, −3).
And, radius = \[\sqrt{18} = 3\sqrt{2}\]