Given that the circle C ': (x-1) ^ 2 + y ^ 2 = a passes through the origin and is symmetric to the circle C with respect to the straight line y = - x, find the equation of the circle C and the length of the chord where the circle C intersects with the circle C' | Math enthusiast | Mathematical art

Given that the circle C ': (x-1) ^ 2 + y ^ 2 = a passes through the origin and is symmetric to the circle C with respect to the straight line y = - x, find the equation of the circle C and the length of the chord where the circle C intersects with the circle C'

Through the origin, a = 1, C 'is a circle whose point is at (1,0) radius 1,
Circle C and circle C 'are symmetric with respect to the line y = - X,
That is, the circle point is symmetric with respect to the straight line y = - x, and the circle point of circle C is (0, - 1),
The equation of circle C is X & sup2; + (y + 1) & sup2; = 1,
Obviously, the intersection point of two circles passing through the straight line y = - x is (0,0) (1, - 1)
The distance between the two points is the length of the intersecting chord, which is 2

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