The centre of the circle lies on the line and cuts orthogonally the circle

MATHEMATICS · Subjective · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

The centre of the circle S=0S=0 lies on the line 2x−2y+9=02x-2y+9=0 and S=0S=0 cuts orthogonally the circle x2+y2=4x^2+y^2=4. Show that the circle S=0S=0 passes through two fixed points and find their coordinates.

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