Question

write the equation of the circle centered at $(-2,5)$ with diameter 18.

Explanation:

Step1: Recall the 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: Find the radius

Given the diameter is \(18\), the radius \(r\) is half of the diameter. So \(r=\frac{18}{2}=9\).

Step3: Substitute the center and radius into the formula

The center of the circle is \((-2, 5)\), so \(h = -2\) and \(k = 5\), and \(r = 9\). Substituting these values into the circle equation formula: \((x - (-2))^2 + (y - 5)^2 = 9^2\), which simplifies to \((x + 2)^2 + (y - 5)^2 = 81\).

Answer:

\((x + 2)^2 + (y - 5)^2 = 81\)