the equation of the circle with diameter at (2,2) and (8,14) is (x-5)^2 + (y - 8)^2 = 45
How to calculate the equation of a circle?
A circle is a 2-dimensional shape with no edges.
The standard equation of a circle with centre (a, b) and radius "r" is given as:
(x-a)^2 + (y-b)^2 = r^2
Given the diameter of circle with coordinate (2,2) and (8,14), the diameter is expressed as:
D = √12² + 6²
D = √144+36
D = √180
For the radius
r = √180/2
r² = 180/4
r² = 45
Determine the centre (a, b)
(a, b) = (2+8/2 2+14/2)
(a, b) = (5, 8)
Substitute
(x-5)^2 + (y - 8)^2 = 45
Hence the equation of the circle with diameter at (2,2) and (8,14) is (x-5)^2 + (y - 8)^2 = 45
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