已知M(-2,0),N(2,0),则以MN为斜边的直角三角形的直角顶点P

已知M(-2,0),N(2,0),则以MN为斜边的直角三角形的直角顶点P的轨迹方程是(  )

A.x2+y2=2

B.x2+y2=4

C.x2+y2=2(x≠±2)

D.x2+y2=4(x≠±2)

答案

D


解析:

P(x,y),由于PMN为三角形,∴y≠0.

又∵PMPN,

.

y2=4-x2.

x2+y2=4.

y≠0,∴x≠±2.

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