Question

write the equation of the circle centered at (7, -1) with diameter 18.

Explanation:

Step1: Find the radius

The radius \(r\) of a circle is half of the diameter. Given diameter \(d = 18\), then \(r=\frac{d}{2}=\frac{18}{2}=9\).

Step2: Use the standard form of the circle 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 of the circle. Here, \(h = 7\), \(k=-1\) and \(r = 9\).
Substitute these values into the formula: \((x - 7)^2+(y+ 1)^2=9^2\).

Answer:

\((x - 7)^2+(y + 1)^2=81\)