Write the equation of the circle with a center at (2,-2) and point (6,1)

6^5

Can you explain please? Like do i just substitute the points into the equation and solve it.

To find the equation of a circle, we'll use the general equation for a circle which is:

(x - a)^2 + (y - b)^2 = r^2

where (a, b) represents the center of the circle, and r represents the radius.

Given that the center of the circle is (2, -2), we have a = 2 and b = -2. Now, let's find the radius of the circle.

The radius can be found by calculating the distance between the center of the circle and any point on the circumference. In this case, the given point (6, 1) lies on the circumference of the circle. So,

Using the distance formula:
r = √((x2 - x1)^2 + (y2 - y1)^2)
= √((6 - 2)^2 + (1 - (-2))^2)
= √(4^2 + 3^2)
= √(16 + 9)
= √25
= 5

Now that we have the center coordinates (2, -2) and the radius r = 5, we can write the equation of the circle:

(x - 2)^2 + (y - (-2))^2 = 5^2
(x - 2)^2 + (y + 2)^2 = 25

Therefore, the equation of the circle with a center at (2, -2) and a point (6, 1) is (x - 2)^2 + (y + 2)^2 = 25.