Question

What is the center and radius of the circle defined by x² + y² -4x + 8y = 7?

Answer 1

Answer:

(2, -4) and √27

Step-by-step explanation:

To make perfect squares on the left, we add constants 4 and 16 to both the sides,

${x}^{2} - 4x + 4 + {y}^{2} + 8y + 16 = 4 + 16 + 7$

${(x - 2)}^{2} + {(y + 4)}^{2} = 27$

So, centre is

(2, -4)

and radius is

$\sqrt{27}$