Question

find the equation of a circle satisfying the given conditions. center (5, 4), radius $sqrt{5}$ the equation of the circle in standard form is . (type an equation.)

Explanation:

Step1: Recall circle - standard form

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: Identify values of $h$, $k$, and $r$

Given that the center is $(5,4)$, so $h = 5$, $k = 4$, and the radius $r=\sqrt{5}$.

Step3: Substitute values into the formula

Substitute $h = 5$, $k = 4$, and $r=\sqrt{5}$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 5)^2+(y - 4)^2=(\sqrt{5})^2$.

Step4: Simplify the equation

Since $(\sqrt{5})^2 = 5$, the equation of the circle is $(x - 5)^2+(y - 4)^2=5$.

Answer:

$(x - 5)^2+(y - 4)^2=5$