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:

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?