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.y2=-16x                            B.y2=-32x

C.y2=16x                             D.y2=16xy=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PF(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y2=16x.

答案:

C

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