25 points available
1.
identify the center and the radius of a circle with equation (x + 3)² + y² = 9
format your answer as: (x, y), r
2.
write the equation of a circle with center at (-4,3) and r = 6.
3.
write the equation of a circle with the endpoints of the diameter at (-1, 6) and (5, -4). watch the signs!

Step-by-step explanation:

The equation of a circle in standard form:

(h, k) - center

r - radius

1. We have the equation:

2. We have the center (-4, 3) and the radius r = 6. Substitute:

3. We have the endpoints of the diameter: (-1, 6) and (5, -4).

Midpoint of diameter is a center of a circle.

The formula of a midpoint:

Substitute:

The center is in (2, 1).

The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.

The formula of a distance between two points:

Substitute the coordinates of the points (2, 1) and (5, -4):

Finally we have:

here is a big fat