Question

Find the center and radius of the circle represented by the equation below. left bracket, x, plus, 15, right bracket, squared, plus, left bracket, y, minus, 14, right bracket, squared, equals, 361 (x+15) 2 +(y−14) 2 =361

Answer 1

The center of the circle is (-15, +14), and its radius is 19 units.

Step-by-step explanation:

To find the center and radius of the circle represented by the equation \((x+15)^2 + (y-14)^2 = 361\), 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 of the circle and \(r\) is its radius.

The given equation is already in this form, so we can directly read off the center and radius. The center \((h,k)\) is found by taking the opposite sign of the numbers inside the brackets with \(x\) and \(y\), which gives us \((-15, +14)\). The radius \(r\) is the square root of the number on the right side of the equation, so \(r = \sqrt{361} = 19\).