Quick! Given the moving circle ⊙ P and ⊙ F1: (x + 5) + y = 36, and passing through the point F2 (5,0), find the trajectory equation in the center of the moving circle [please write down the process of solution and analysis!]

Quick! Given the moving circle ⊙ P and ⊙ F1: (x + 5) + y = 36, and passing through the point F2 (5,0), find the trajectory equation in the center of the moving circle [please write down the process of solution and analysis!]

1) It is known that point F1 (- 5,0), R ^ 2 = 36 = 6 ^ 2, r = 6.2). The center of moving circle P (x, y), radius r.3). | Pf1 | - | PF2 | = (6-r) - r = 6, the locus of point P is hyperbola, the real axis is on ox, 2A = 6, a = 3. C = | F1F2 | / 2 = [5 - (- 5)] / 2 = 10 / 2 = 5.4). B ^ 2 = C ^ 2-A ^ 2 = 5 ^ 2-3 ^ 2 = 25-9 = 16, the locus obtained is (x ^ 2 / 9) - (y ^ 2 / 16) = 1

Given that the fixed circle F1: x2 + Y2 + 10x + 24 = 0, the fixed circle F2: x2 + y2-10x + 9 = 0, the moving circle m and the fixed circles F1 and F2 are circumscribed, the trajectory equation of the moving circle center m is obtained
The answer is x ≤ - 3. Why

Circle F1: x2 + Y2 + 10x + 24 = 0, center F1 (- 5,0), radius 1, circle F2: x2 + y2-10x + 9 = 0, center F2 (5,0), radius 4. If the radius of the moving circle is r, then | MF1 | = R + 1, | MF2 | = R + 4, so | MF2 | - | MF1 | = 3, it represents the left branch of the hyperbola, so x ≤ - 3 / 2, because 2A = 3, C = 5, so B & # 178; = C & # 178; - A & # 17