If a circle passing through the point (1,0) touches y-axis at (0,2), then the length of the chord of the circle along the x-axis is

Since the required circle touches y-axis at (0,2) and let r be the radius of the circle. So, the center will be (-r,2).
The equation of the circle is given by:
(x+r)² + (y-2)² = r²
Since the circle passes through (1,0), we have:
(1+r)² + (0-2)² = r²
1 + 2r + r² + 4 = r²
2r + 5 = 0
2r = -5
r = -5/2
The center of the circle is (5/2, 2).
The equation of the circle is:
(x - 5/2)² + (y - 2)² = (5/2)²
To find the length of the chord along the x-axis, we set y = 0:
(x - 5/2)² + (0 - 2)² = (5/2)²
(x - 5/2)² + 4 = 25/4
(x - 5/2)² = 25/4 - 16/4
(x - 5/2)² = 9/4
x - 5/2 = ±3/2
x = 5/2 ± 3/2
x = 4 or x = 1
The length of the chord along the x-axis is 4 - 1 = 3