Equate a circle, one of the diameters of which is a line segment with ends A (-3; -2) B (5; 4).
| February 12, 2021 | education
The equation of the circle is (x – x0) ^ 2 + (y – y0) ^ 2 = R².
The radius is half the diameter. We calculate the length of the diameter AB:
AB = √ ((- 3 – 5) ² + (-2 – 4) ²) = √ (64 + 36) = √100 = 10.
Hence, the radius is 10/2 = 5.
Point O (the center of the circle) is in the middle of the line segment AB. Let O have coordinates (x0; y0).
x0 = (5 + (-3)) / 2 = 2/2 = 1.
y0 = (4 + (-2)) / 2 = 2/2 = 1.
The center of the circle has coordinates O (1; 1).
We compose the equation of the circle:
(x – 1) 2 + (y – 1) 2 = 25.
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