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若点P到定点F(4,0)的距离比它到直线x+5=0的距离小1,则点P的轨迹方
若点P到定点F(4,0)的距离比它到直线x+5=0的距离小1,则点P的轨迹方
若点
P
到定点
F
(4,0)的距离比它到直线
x
+5=0的距离小1,则点
P
的轨迹方程是( )
A.
y
2
=-16
x
B.
y
2
=-32
x
C.
y
2
=16
x
D.
y
2
=16
x
或
y
=0(
x
<0)
答案
解析:
∵点
F
(4,0)在直线
x
+5=0的右侧,且
P
点到点
F
(4,0)的距离比它到直线
x
+5=0的距离小1,∴点
P
到
F
(4,0)的距离与到直线
x
+4=0的距离相等.故点
P
的轨迹为抛物线,且顶点在原点,开口向右,
p
=8,故
P
点的轨迹方程为
y
2
=16
x
.
答案:
C
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