Find the equation of the circle that passes through the point of intersection of the circles x^2+y^2=2x, x^2+y^2=2y and contains the point (2,1)

Question

Tge equation of the circle is in the form of (x-h )^2+(y-k) ^2=r^2.

Answer 1

x² + y²  = 2x ⇒ x² - 2x + y² = 0

x² - 2x + 1 + y² = 1

(x - 1)² + y² = 1

 

x² + y² = 2y ⇒ x² + y² - 2y = 0

x² + y² - 2y + 1 = 1

x² + (y - 1)² = 1

 

The two circles have two points on intersection: (0, 0) and (1, 1)

Review the data in your post and make necessary additions.