若曲线c1:x^2-y^2=0与c2(x-a)^2+y^2=1的图像有三个交点,则a=急

Question

若曲线c1:x^2-y^2=0与c2(x-a)^2+y^2=1的图像有三个交点,则a= 急

Answer 1

二者均关于x轴对称, 要使圆和双曲线有3个共同点,只须圆过和圆心(a, 0)异侧的双曲线顶点(此时在同侧有两个交点).
(i) a > 0, 圆过(-1, 0)
(-1 - a)^2 + 0 = 1
a = 0或a = -2均舍去
(ii) a < 0, 圆过(1, 0)
(1 - a)^2 + 0 = 1
a = 0 (舍去)或a =2
a = 2