Question

write the standard form of the equation of the circle with the given center and radius.
center (6, - 1), r = √3
the equation of the circle in standard form is □
(simplify your answer.)

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Substitute the given values

Here, \(h = 6\), \(k=-1\), and \(r = \sqrt{3}\). Substituting these into the formula gives \((x - 6)^2+(y-(-1))^2=(\sqrt{3})^2\).

Step3: Simplify the equation

Simplify \((y - (-1))\) to \((y + 1)\) and \((\sqrt{3})^2\) to \(3\). So the equation becomes \((x - 6)^2+(y + 1)^2=3\).

Answer:

\((x - 6)^2+(y + 1)^2=3\)