Questions: Write the standard form of the equation of the circle with its center at (-2,0), and a radius of 3. What is the equation of the circle in standard form?

Solution Steps

To find the standard form of the equation of a circle, we use the formula \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius. Given the center \((-2, 0)\) and radius \(3\), we substitute these values into the formula to get the equation.

The center of the circle is given as \((-2, 0)\) and the radius is \(3\).

The standard form of the equation of a circle is given by:

\[ (x - h)^2 + (y - k)^2 = r^2 \]

where \((h, k)\) is the center and \(r\) is the radius.

Substituting the values of the center and radius into the equation:

\[ (x - (-2))^2 + (y - 0)^2 = 3^2 \]

This simplifies to:

\[ (x + 2)^2 + y^2 = 9 \]

Final Answer