Question

当a为何值时,直线x+y-2a+1=0与圆x^2+y^2-2x+4y+1=0相切?相离?相交?

当a为何值时,直线x+y-2a+1=0与圆x^2+y^2-2x+4y+1=0相切?相离?相交?

Answer 1

圆方程可变为
(x
-
1)²
+
(y
+
2)²
=
4,
圆心C(1,
-2),
半径r
=
2
C与直线的距离d
=
|1
-
2
-
2a
+
1|/√2
=
√2|a|
(1)
相切
d
=
r,
√2|a|
=
2,
a
=
±√2
(2)
相离
d
>
r
√2|a|
>
2,
a
>
√2
或
a
<
-
√2
(3)相交
d
<
r
√2|a|
<
2,
-√2
<
a
<
√2