Questions: A circle has a radius of √131 units and is centered at (0,-4.3). Write the equation of this circle.

Solution Steps

To write the equation of a circle, we use the standard form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. Here, the center is \((0, -4.3)\) and the radius is \(\sqrt{131}\).

The circle is centered at \((0, -4.3)\) with a radius of \(\sqrt{131}\).

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

Substitute \(h = 0\), \(k = -4.3\), and \(r = \sqrt{131}\) into the equation: \[ (x - 0)^2 + (y + 4.3)^2 = (\sqrt{131})^2 \]

Simplify the equation: \[ x^2 + (y + 4.3)^2 = 131 \]

Final Answer