The equation of circle A circle is tangent to the y-axis, the center of the circle is on the straight line x-3y = 0, and the chord length obtained by cutting the circle with the straight line y = x is 2 and the root sign is 7

The equation of circle A circle is tangent to the y-axis, the center of the circle is on the straight line x-3y = 0, and the chord length obtained by cutting the circle with the straight line y = x is 2 and the root sign is 7

X * 2 + y * 2 = R * 2, center O (0,0), radius R;
(x-a) 2 + (y-b) 2 = R2, center O (a, b), radius R
Conditions for determining the circular equation
In the standard equation of circle (x-a) 2 + (y-b) 2 = R2, there are three parameters a, B and R. as long as a, B and R are solved, then the equation of circle will be determined. Therefore, to determine the equation of circle, three independent conditions are required, in which the center of circle is the locating condition of circle and the radius is the setting condition of circle
Methods and steps of determining the equation of circle
The main method to determine the equation of a circle is the method of undetermined coefficient, that is, to list the equations of a, B and R, to find a, B and R, or to find the center (a, b) and radius r directly
According to the meaning of the problem, let the standard equation (x-a) 2 + (y-b) 2 of the circle be R2;
According to the known conditions, the equations of a, B and R are established;
By solving the equations, finding out the values of a, B and R, and substituting them into the set equations, we can get the equation of the circle