Question

write the standard form of the equation of the circle with the given center and radius. center (5, -2), r = 3 type the standard form of the equation of the circle. (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 \(h = 5\), \(k=-2\), and \(r = 3\). Substitute these into \((x - h)^2+(y - k)^2=r^2\).
We get \((x - 5)^2+(y-(-2))^2=3^2\).

Step3: Simplify the equation

Simplify \((y-(-2))\) to \((y + 2)\) and \(3^2\) to \(9\). So the equation is \((x - 5)^2+(y + 2)^2=9\).

Answer:

\((x - 5)^2+(y + 2)^2=9\)