Question

write the standard form of the equation of the circle with the given center and radius. center (5, - 3), ( r = sqrt{5} ) 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 \(h = 5\), \(k=-3\), and \(r = \sqrt{5}\). Substitute these into the formula:

$$
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$$

Answer:

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