已知X型的椭圆标准方程,那么如何设与它共焦点的双曲线方程?为什么?
\u5df2\u77e5\u692d\u5706\u7cfb\u65b9\u7a0b\uff0c\u4e0e\u5b83\u5171\u7126\u70b9\u7684\u53cc\u66f2\u7ebf\u7cfb\u5982\u4f55\u8bbe\u5982\u679c\u692d\u5706\u7684\u7126\u70b9\u5728\u957f\u8f74\uff0c\u540c\u7406 \u53cc\u66f2\u7ebf\u7684\u5b9e\u8f74\u5219\u5728x\u8f74\uff0c\u692d\u5706\u4e0e\u53cc\u66f2\u7ebf\u7684\u79bb\u5fc3\u7387\u4e0d\u53ef\u80fd\u76f8\u7b49\uff0c\u692d\u5706\u7684\u79bb\u5fc3\u7387\u4e3ae=c\a\uff0801\uff09\u4e0e\u692d\u5706\u5173\u6ca1\u6709\u4ea4\u96c6\u3002\u53cc\u66f2\u7ebf\u4e0e\u692d\u5706\u7684\u5173\u7cfb\u6700\u597d\u7ed3\u5408\u56fe\u7247\u770b\uff0c\u6211\u8fd9\u91cc\u8fd8\u6ca1\u6709\u6743\u9650\u8d34\u56fe\u7247\uff0c\u4f60\u53ef\u4ee5\u767e\u5ea6\u4e00\u4e0b\u7ed3\u5408\u7740\u770b\u3002
\u89e3\uff1ac^2\u5df2\u77e5
\u8bbe\u4e3ax^2/a^2-y^2/(c^2-a^2)=1
\u5982\u6709\u7591\u95ee\uff0c\u53ef\u8ffd\u95ee\uff01
焦点为(c,0) (-c,0)
c^2=a^2-b^2
x^2/d^2-y^2/e^2=1
d^2+e^2=c^2
d^2+e^2=a^2-b^2
就共焦点了
绛旓細妞渾鐨勬爣鍑嗘柟绋嬪叡鍒嗕袱绉嶆儏鍐 锛氬綋鐒︾偣鍦x杞存椂锛屾き鍦嗙殑鏍囧噯鏂圭▼鏄細x^2/a^2+y^2/b^2=1锛(a>b>0)锛涘綋鐒︾偣鍦▂杞存椂锛屾き鍦嗙殑鏍囧噯鏂圭▼鏄細y^2/a^2+x^2/b^2=1锛(a>b>0)锛
绛旓細c^2=a^2-b^2 c
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