Answered

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

Verified Answer :

LammettHash

\(x^2+y^2+x=0\iff~x^2+x+\dfrac14+y^2=\dfrac14\iff~\left(x+\dfrac12\right)^2+y^2=\left(\dfrac12\right)^2\)

which is the equation for a circle of radius \(\dfrac12\) centered at \(\left(-\dfrac12,0\right)\).

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