Question

write the standard form of the equation of the circle with the given center and radius. center $(4,5)$, $r = \sqrt{6}$ 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 of the circle and \(r\) is the radius.

Step2: Substitute the given values into the formula

Given \(h = 4\), \(k = 5\), and \(r=\sqrt{6}\). Substitute these into the formula: \((x - 4)^2+(y - 5)^2=(\sqrt{6})^2\).

Step3: Simplify the right - hand side

Since \((\sqrt{6})^2=6\), the equation becomes \((x - 4)^2+(y - 5)^2=6\).

Answer:

\((x - 4)^2+(y - 5)^2=6\)