Question

Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle.

x2 + y2 + x = 0
standard form
center (x, y) = ( )
radius

Answer 1

`x^2+y^2+x=0\iff~x^2+x+\frac14+y^2=\frac14\iff~\left(x+\frac12\right)^2+y^2=\left(\frac12\right)^2`

which is the equation for a circle of radius
`\frac12` centered at
`\left(-\frac12,0\right)`.