Answer:
(x - 12)² + y² = 100
Explanation:
The standard form of the equation of a circle is;
(x - a)² + (y - b)² = r²
where:
a and b are the coordinates of the centre of the circle
r is the radius
We are given the coordinates of the endpoints of the diameter as; (22,0) and (2,0)
Thus, the centre of the circle would be at the mid point of the endpoints of the diameter.
Coordinates of the centre is;
((22 + 2)/2), (0 +0)/2))
This is;
(12, 0)
So, a = 12 and b = 0
Now,to get the radius r, we will use the formula;
r = √[(x2 - x1)² + (y2 - y1)²]
Where;
(x1, y1) and (x2, y2) are 2 points namely (12,0) and (22, 0)
r = √[(12 - 22)² + (0 - 0)²]
r = √(-10)²
r = √100
r = 10
Thus,equation of the circle is;
(x - 12)² + (y - 0)² = 10²
(x - 12)² + y² = 100