Question

A circle has the equation (x−13)2+(y−1)2=4.

A: What is the center of the circle?
B: What is the radius of the circle?

Select two answers: one for question A, and one for question B.

A: (13,1)

B: 4

A: (−13,−1)

A: (−13,1)

A: (13,−1)

B: 2

B: 2–√

Answer 1

The center of the given circle is at (13, 1), and the radius of the circle is 2.

Step-by-step explanation:

The equation of a circle is generally given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Looking at the given equation (x - 13)^2 + (y - 1)^2 = 4, we can see that it is already in this standard form.

To answer the questions:

The center of the circle is (13, 1), which comes from the terms within the parentheses being subtracted from x and y.

The radius of the circle is not simply 4, as one might surmise by a quick glance. Instead, the equation gives us the radius squared, r^2 = 4. Taking the square root of both sides, we find that the radius, r, is 2.

Answer 2

An equation of circle has form

`(x-x_0)^2+(y-y_0)^2=r^2 \\ where\: x_0\: and\: y_0\: are\: the\: center`

So, the center is (13;1)

Now we need to find a radius

Let's create an equation

`{r}^(2) = 4 \\ r = √(4) \\ r = 2`

So radius is 2