We consider (Cm) all points M (x, y) such that: x ² + y ²-mx + my +2 m-2 = 0 (m is a real parameter) 1) Discuss the values of m]-l infinite, 2 [U] 2, + infinite [the nature of (Cm). Assume that m does not equal 2. 2) a) Show that (Cm) is a circle. b) determine the set of centers of circles (Cm) when m changes in] the infinite-2 [U] 2, + infinite [c) Prove that all circles (Cm) pass through the same point A we must seek

Question

We consider (Cm) all points M (x, y) such that: x ² + y ²-mx + my +2 m-2 = 0 (m is a real parameter) 1) Discuss the values ​​of m]-l infinite, 2 [U] 2, + infinite [the nature of (Cm). Assume that m does not equal 2. 2) a) Show that (Cm) is a circle. b) determine the set of centers of circles (Cm) when m changes in] the infinite-2 [U] 2, + infinite [c) Prove that all circles (Cm) pass through the same point A we must seek