Question

圆的一动圆与已知圆O1（x+3）²+y²=1外切，与圆O2（x-3）²+y²=81内切，

试求动圆圆心的轨迹方程

Answer 1

求动圆圆心M的轨迹L的方程

Answer 2

O₁(-3, 0), r₁ = 1
O₂(3,0), r2 = 9
设圆心C(x, y), 半径r
CO₁ = √[(x + 3)² + (y- 0)²] = √[(x + 3)² + y²] = r + r₁ = r+1 (1)
CO₂ = √[(x - 3)² + (y- 0)²] = √[(x - 3)² + y²] = r₂ - r = 9 - r (2)
(1)+(2):
√[(x + 3)² + y²] + √[(x - 3)² + y²] = 10
整理得:
x²/25 + y²/16 = 1 (椭圆)