顶点在原点,坐标轴为对称轴的抛物线,过点(-2,3),则它的方程

顶点在原点,坐标轴为对称轴的抛物线,过点(-2,3),则它的方程是

A.x2=-yy2=x                                      B.y2=-xx2=y

C.x2=y                                                         D.y2=-x

答案

解析:∵抛物线的顶点在原点,坐标轴为对称轴,

∴抛物线的方程为标准形式.

当抛物线的焦点在x轴上时,

∵抛物线过点(-2,3),

∴设抛物线的方程为y2=-2px(p>0).

∴32=-2p(-2).∴p=.

∴抛物线的方程为y2=-x.

当抛物线的焦点在y轴上时,

∵抛物线过点(-2,3),

∴设抛物线的方程为x2=2py(p>0).

∴(-2)2=2p·3.∴p=.

∴抛物线的方程为x2=y.

答案:B

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