Questions: Given the center and radius, write the standard equation for the circle. Center: (-5,2) Radius: 6 (x+5)^2+(y-2)^2=6 (x+5)^2+(y-2)^2=6^2 (x-5)^2+(y-2)^2=6^2 (x+5)^2+(y+2)^2=6^2

Solution Steps

To write the standard equation of a circle given its center and radius, use the formula \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. Substitute the given center \((-5, 2)\) and radius \(6\) into this formula to find the correct equation.

The center of the circle is given as \((-5, 2)\) and the radius is \(6\).

The standard 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:

\[ h = -5, \quad k = 2, \quad r = 6 \]

This gives us:

\[ (x - (-5))^2 + (y - 2)^2 = 6^2 \]

which simplifies to:

\[ (x + 5)^2 + (y - 2)^2 = 36 \]

Final Answer