轨迹方程X2+y2=2(m+3)x+2(1-4m2)y+16m2+9=0表示圆,求圆心C的轨迹方程
x^2 + y^2 + 2(m+3)x + 2(1-4m^2) + 16m^2 + 9 = 0;
(x+(m+3))^2 + (y+(1-4m^2))^2 = r^2
r^2 = (m+3)^2 + (4m^2-1)^2 - 16m^2 -9
= 16m^4 -23m^2 + 6m+1
= 16(m^2 -1)^2 + 9(m+1/3)^2 -16>0
圆心( -m-3, 4m^2-1); 设圆心(x,y);
x = -m-3;
y = 4m^2-1;
m = -3-x,
y = 4m^2-1
= 4(x+3)^2 -1
圆心轨迹方程是抛物线。
x满足约束:
16((x+3)^2 -1...全部
x^2 + y^2 + 2(m+3)x + 2(1-4m^2) + 16m^2 + 9 = 0;
(x+(m+3))^2 + (y+(1-4m^2))^2 = r^2
r^2 = (m+3)^2 + (4m^2-1)^2 - 16m^2 -9
= 16m^4 -23m^2 + 6m+1
= 16(m^2 -1)^2 + 9(m+1/3)^2 -16>0
圆心( -m-3, 4m^2-1); 设圆心(x,y);
x = -m-3;
y = 4m^2-1;
m = -3-x,
y = 4m^2-1
= 4(x+3)^2 -1
圆心轨迹方程是抛物线。
x满足约束:
16((x+3)^2 -1)^2 + 9(x+8/3)^2 -16>0。收起