Question

The equation of a circle is given below. (x-0.5)^{2}+(y-3.5)^{2} = 16(x−0.5) 2 +(y−3.5) 2 =16left parenthesis, x, minus, 0, point, 5, right parenthesis, squared, plus, left parenthesis, y, minus, 3, point, 5, right parenthesis, squared, equals, 16 What is its center? ((left parenthesis ,,comma ))right parenthesis What is its radius? If necessary, round your answer to two decimal places. units

Answer 1

The radius is 4 units long.

Explanation:

The given equation is

`(x-0.5)^(2) +(y-3.5)^(2) =16`

This equation belongs to a circle, which center is at (0.5, 3.5) and its radius is 4.

You can deduct its elements, becase this equation of the circle is explicit, which means the constant term represents the square power of the radius. Solving that, we have

`r^(2) = 16\\r=√(16)\\ r=4`

Therefore, the radius is 4 units long.