find the center and radius of the circle. Write in equation form. (4,8) and (13,8)
two points do not determine a circle. More is needed.
To find the center and radius of a circle given two points on its circumference, you can use the midpoint formula and distance formula.
First, let's find the midpoint of the line segment between the two given points. The midpoint is the average of the x-coordinates and the average of the y-coordinates.
Midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Using the given points (4,8) and (13,8), we can substitute these values into the midpoint formula:
Midpoint = ((4 + 13) / 2, (8 + 8) / 2)
Midpoint = (17 / 2, 16 / 2)
Midpoint = (8.5, 8)
Hence, the center of the circle is (8.5, 8).
Next, let's find the radius of the circle. The radius is the distance between the center of the circle and one of the given points. We can use the distance formula to calculate it.
Distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the center (8.5, 8) and one of the given points (4,8), we substitute these values into the distance formula:
Distance = √((4 - 8.5)^2 + (8 - 8)^2)
Distance = √((-4.5)^2 + 0^2)
Distance = √(20.25)
Distance = 4.5
Hence, the radius of the circle is 4.5.
Finally, we can write the equation of the circle in standard form using the center (h, k) and the radius (r):
Equation of a circle: (x - h)^2 + (y - k)^2 = r^2
Plugging in the values, we get:
Equation: (x - 8.5)^2 + (y - 8)^2 = 4.5^2