please help me with part A of this question

3. In this exercise, we will study the critical points of the function 1 p. 7'2 p 2(1 + may wherer= w2+y2,p= y/(aca)2+y2,R= x/(a:+,ua)2+y2,anda>0andu20 are real parameters. This function is dened in Q = R2 \\ {(ua, 0), (a, 0)}, and appears as the effective potential eld for a test mass (satellite) moving in the gravitational eld generated by a small body (Earth) at (a, 0) and a large body (Sun) at (,ua,0), with respect to the coordinate system that is following the rotation of both bodies. In particular, in this coordinate system, the two bodies are xed, but the rotation of the coordinate system manifests itself through the centrifugal term m. With respect to a nonrotating coordinate system, the two bodies would be circling around their common centre of mass, which is the origin in our rotating coordinate system any. The parameter ,u is assumed to be small, and it represents the mass ratio between the bodies. (a) Show that u has exactly one critical point of the form p1 = (x1, 0) with 321