Question

write the standard form of the equation of the circle with the given center and radius. center (-5, -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 the equation of a circle 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 into the formula

Given \(h=-5\), \(k = - 1\), and \(r=\sqrt{3}\).
Substitute into the formula: \((x-(-5))^2+(y-(-1))^2=(\sqrt{3})^2\).

Step3: Simplify the equation

Simplify \((x + 5)^2+(y + 1)^2=3\).

Answer:

\((x + 5)^2+(y + 1)^2=3\)