Questions: Write the standard form of the equation of the circle with the given center and radius. Center (3,4), r=5 Type the standard form of the equation of the circle. (Simplify your answer.)

Solution Steps

The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is given by:

\[ (x - h)^2 + (y - k)^2 = r^2 \]

Given the center \((3, 4)\) and radius \(r = 5\), substitute these values into the standard form equation:

\[ (x - 3)^2 + (y - 4)^2 = 5^2 \]

Calculate \(5^2\):

\[ 5^2 = 25 \]

Substitute back into the equation:

\[ (x - 3)^2 + (y - 4)^2 = 25 \]

Final Answer