Question

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.)

Explanation:

Step1: Recall circle - equation formula

The standard - form 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 given values

Given that $h = 3$, $k = 4$, and $r = 5$, we substitute these values into the formula: $(x - 3)^2+(y - 4)^2=5^2$.

Step3: Simplify the right - hand side

$5^2=25$, so the equation of the circle is $(x - 3)^2+(y - 4)^2=25$.

Answer:

$(x - 3)^2+(y - 4)^2=25$