The equation of a circle with a line segment length of 10 on the x-axis through the origin and point m (1, - 1) is obtained The equation of a circle with a line segment length of 10 on the x-axis through the origin and point m (1, - 1) is obtained

The equation of a circle with a line segment length of 10 on the x-axis through the origin and point m (1, - 1) is obtained The equation of a circle with a line segment length of 10 on the x-axis through the origin and point m (1, - 1) is obtained

∵ the length of the section on the x-axis is 10 and over (0,0)
If there is another point (10,0) or (- 10,0) on the x-axis, then the center of the circle is O (5, b) or o '(- 5, B')
The circular equation is O: (X-5) ^ 2 + (y-b) ^ 2 = R ^ 2 or (x + 5) ^ 2 + (y-b ') ^ 2 = R' ^ 2
Substituting coordinates: (0,0); (1, - 1)
=> 25+b^2=r^2 25+b'^2=r'^2
16+1+2b+b^2=r^2 or 36+1+2b'+b'^2=r'^2
=> b=2 r^2=29 ； b'=-6 r'^2=61
The equations (X-5) ^ 2 + (Y-2) ^ 2 = 29 and (x + 25) ^ 2 + (y + 6) ^ 2 = 61 are obtained