取BC中点为原点,BC为x轴.则B（-3,0）,C(3,0).由题意（三角形ABC的周长等于16）可知AB+AC = 16 - BC = 10到此不难发现A点轨迹应为一椭圆.且2a = 10,a = 5；2c = 6 ,c = 3则b^2 = a^2 - c^2 = 16故所求方程即为x^2/25 ...