Question

和点O(0,0),A(c,0)距离的平方差为常数c的轨迹方程为?

Answer 1

设P(x,y),

PO^2=x^2+y^2

PA^2=x^2-2cx+c^2+y^2

|PO^2-PA^2|=c

|2cx-c^2|=c

4c^2x^2-4c^3x+c^4=c^2

c=0,不合题意,c≠0

4x^2-4cx+c^2-1=0

[2x-(c+1)][2x-(c-1)]=0

∴x=(c+1)/2,x=(c-1)/2 .