Question

Find the center and radius of the circle with the equation. Please show work!

Answer 1

(1, -2)

Explanation:

The equation of a circle:

`(x-h)^2+(y-k)^2=r^2`

(h, k) - center

r - radius

We have:

`x^2-2x+y^2+4y=4\qquad\text{add}\ 1^2\ \text{and}\ 2^2\ \text{to both sides}\\\\x^2-2x+1^2+y^2-2(-2)(y)+2^2=2(1^2)(2^2)\qquad\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2\\\\(x-1)^2+(y-(-2))^2=8\\\\h=1,\ k=-2\to(1,\ -2)`