Question

Find the centre and radius of the circle x² + y² – 2x + 4y = 8

Answer 1

We write the given equation in the form (x² – 2x) + (y² + 4y) = 8

Now, completing the squares, we get

(x² – 2x + 1) + (y² + 4y + 4) = 8 + 1 + 4

(x – 1)² + (y + 2)² = 13

Comparing it with the standard form of the equation of the circle

We see that the centre of the circle is (1, –2) and radius is `sqrt(13)`.