Question

What are the center radius form of a circle defined by x²+y²–2x+4y–1=0

Answer 1

$$x^2+y^2-2x+4y-1=0$$

$$(x^2-2x+1)+(y^2+4y+4)=6$$

$$(x-1)^2+(y+2)^2=(\sqrt{6})^2$$

The center-radius form of the circle equation is

$$(x-1)^2+(y+2)^2=(\sqrt{6})^2,$$

with the center at $(1, -2)$ and the radius $\sqrt{6}.$