Question

what is the coordinate of the center in the given equation?
x² + (y + 3)² = 90

Explanation:

Step1: Recall circle equation form

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step2: Rewrite given equation

Given equation: \(x^2 + (y + 3)^2 = 90\). Rewrite \(x^2\) as \((x - 0)^2\) and \((y + 3)^2\) as \((y - (-3))^2\). So it matches \((x - 0)^2 + (y - (-3))^2 = 90\).

Step3: Identify center coordinates

From the standard form, \(h = 0\) and \(k = -3\), so the center is \((0, -3)\).

Answer:

\((0, -3)\)