Questions: What is the center and radius of (x+10)^2+(y+1)^2=25?

Solution Steps

To find the center and radius of the circle given by the equation \((x+10)^{2}+(y+1)^{2}=25\), we can compare it to the standard form of a circle's equation, \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. In this case, the equation is already in standard form, so we can directly identify the center and radius.

The given equation is \((x+10)^2 + (y+1)^2 = 25\). This is already in the standard form of a circle's equation, which is \((x-h)^2 + (y-k)^2 = r^2\).

In the standard form \((x-h)^2 + (y-k)^2 = r^2\), the center of the circle is \((h, k)\). By comparing, we find:

• \(h = -10\)
• \(k = -1\)

Thus, the center of the circle is \((-10, -1)\).

The radius \(r\) is found by taking the square root of the right side of the equation. Here, \(r^2 = 25\), so: \[ r = \sqrt{25} = 5 \]

Final Answer