Question

what is the radius of the circle ( x^2 + (y + 5)^2 = 100 )? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall the standard circle equation

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: Compare with the given equation

The given equation is \(x^2 + (y + 5)^2 = 100\). Comparing with the standard form, we have \(r^2 = 100\).

Step3: Solve for \(r\)

To find \(r\), we take the square root of both sides: \(r=\sqrt{100}\). Since the radius is a non - negative quantity, \(r = 10\).

Answer:

10