Question

What are the coordinates for the center of the circle and the length of the radius that has an equation of `x^2+y^2-x-2y-11/4=0`?

Answer 1

Center: `(1/2,1)`
Radius: `2`

Explanation:

`x^2+y^2-x-2y-11/4=0`

`rarr color(red)(x^2-x) +color(blue)(y^2-2y) = color(green)(11/4)`

`rarr color(red)(x^2-x+(1/2)^2)+color(blue)(y^2-2y+1)=color(green)(11/4)+color(red)(1/4)+color(blue)(1)`

`rarr color(red)(""(x-1/2))^2+color(blue)(""(y-1))^2=color(green)(2)^2`

which is the standard form for the equation of a circle
with center at `(color(red)(1/2),color(blue)(1))`
and radius `color(green)2`