The equation of the circle with three points P (0,2 times root sign 3) m (1, root sign 7) n (- 2,4) is solved and transformed into standard form

The equation of the circle with three points P (0,2 times root sign 3) m (1, root sign 7) n (- 2,4) is solved and transformed into standard form

The general equation of circle x ^ 2 + y ^ 2 + DX + ey + F = 0
Substituting 3-point coordinates
0 + 12 + 0 + 2 radical 3 * e + F = 0
1 + 7 + D + radical 7 * e + F = 0
4+16-2D+4E+F=0
D=4 E=0 F=-12
The circular equation is: x ^ 2 + y ^ 2 + 4x-12 = 0
Standard form: (x + 2) ^ 2 + y ^ 2 = 4 ^ 2

The equation of the circle with the center at C (2, - 4) and radius root 3 is

(x-2)^2+(y+4)^2=3

Given that the center of the circle is on the x-axis, the radius is 5 and the chord length with a (5,4) as the midpoint is 25, then the equation of the circle is ()
A. (x-3) 2 + y2 = 25B. (X-7) 2 + y2 = 25C. (x ± 3) 2 + y2 = 25d. (x-3) 2 + y2 = 25 or (X-7) 2 + y2 = 25

Let the center of the circle be C (a, 0), the radius of the circle be r = 5, and the length of the chord be BD = 25. According to the vertical diameter theorem, we can get that AC is perpendicular to the chord BD, a (5, 4), a (5-a) 2 + 42 + 5 = 25, a = 3 or a = 7, then the equation of the circle is (x-3) 2 + y2 = 25 or (X-7) 2 + y2 = 25