Final answer:
The distance formula is related to the equation of a circle through its connection to the Center-radius form. The center-radius form of the equation of a circle is given by the equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle and r represents the radius of the circle.
Step-by-step explanation:
The distance formula is related to the equation of a circle through its connection to the Center-radius form. The center-radius form of the equation of a circle is given by the equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle and r represents the radius of the circle.
The distance formula, which is derived from the Pythagorean theorem, can be used to determine the distance between any two points (x1, y1) and (x2, y2) in a coordinate plane. In the context of a circle, if we have the equation of a point (x, y) on the circle and the equation of its center (h, k), we can use the distance formula to find the radius of the circle.
For example, if the equation of a point on a circle is (x - 2)^2 + (y - 3)^2 = 9, and we know that the center of the circle is (2, 3), we can use the distance formula to find the radius:
d = √((x - h)^2 + (y - k)^2)
d = √((x - 2)^2 + (y - 3)^2)
d = √((x - 2)^2 + (y - 3)^2)
d = √((x - 2)^2 + (y - 3)^2)
d = √((x - 2)^2 + (y - 3)^2)
d = 3
Therefore, the radius of the circle is 3.