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数学
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抛物线的顶点在原点,对称轴是坐标轴,且焦点在直线x-y+2=0上,则此抛物线方程为______.
人气:102 ℃ 时间:2019-10-23 05:20:28
解答
直线x-y+2=0交x轴于点A(-2,0),与y轴交于点B(2,0)
①当抛物线的焦点在A点时,设方程为y
2
=-2px,(p>0),可得
p
2
=2,所以2p=8,
∴抛物线方程为y
2
=-8x
②当抛物线的焦点在B点时,设方程为x
2
=2p'y,(p'>0),可得
p′
2
=2,所以2p'=8,
∴抛物线方程为x
2
=8y
综上所述,得此抛物线方程为y
2
=-8x或x
2
=8y
故答案为:y
2
=-8x或x
2
=8y
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