Question

1. determine an equation for the following circle. (note: r - 9)

Explanation:

Step1: Recall circle - equation formula

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 the center of the circle

Given the center of the circle is $(26,4)$, so $h = 26$ and $k = 4$.

Step3: Calculate the radius

The radius $r$ is the distance between the center $(26,4)$ and the point $(3,2)$ on the circle. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, we have $r=\sqrt{(26 - 3)^2+(4 - 2)^2}=\sqrt{23^2+2^2}=\sqrt{529 + 4}=\sqrt{533}$.

Step4: Write the equation of the circle

Substitute $h = 26$, $k = 4$, and $r=\sqrt{533}$ into the standard - form equation: $(x - 26)^2+(y - 4)^2=533$.

Answer:

$(x - 26)^2+(y - 4)^2=533$