Find the center (h, k), the radius r, and the intercepts, if any of each circle. x2 + y2 - 6x + 2y + 6 = 0

a

(h, k) = (3, -1); r = 2; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none

b

(h, k) = (3, -1); r = 4; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none

c

(h, k) = (-3, 1); r = 4; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none

d

(h, k) = (-3, 1); r = 2; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none

e

none

A. , , x-Intercepts: , y-Intercepts: none.

Step-by-step explanation:

Let be the general equation of the circle, we must transform the expression into standard form to determine its center, radius and intercepts. The procedure is shown below:

1)   Given.

2) Commutative and associative properties.

3) Compatibility with addition.

4) Definition of addition/Commutative and associative properties.

5) Perfect square trinomial/Result.

The equation of the circle centered in (h, k) in standard form is defined as:

(Eq. 1)

Where:

, - Coordinate of the center of the circle, dimensionless.

- Radius of the circle, dimensionless.

By direct comparison we find that circle is centered in and has a radius of 2.

Finally, we obtain the intercepts of the given function:

x-Intercepts ()

Roots are found analitically by Quadratic Formula:

y-Intercepts ()

Roots are found analitically by Quadratic Formula:

In a nutshell, there are no y-Intercepts.

We include a graphic including circle, center and x-Intercepts.

Finally, we came to the conclusion that correct answer is A.

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Step-by-step explanation: