求以橢圓x^2/16+y^2/9=1短軸的兩個(gè)頂點(diǎn)為焦點(diǎn),且過(guò)點(diǎn)A(4,-5)的雙曲線的標(biāo)準(zhǔn)方程.
解析：
橢圓短軸在Y軸,故雙曲線焦點(diǎn)在Y軸,其焦點(diǎn)為F1(0,-3),F2(0,3),
設(shè)方程為:y^2/m^2-x^2/n^2=1,
m^2+n^2=9,n^2=9-m^2,
y^2/m^2-x^2/(9-m^2)=1,
A(4,-5)是雙曲線上一點(diǎn),代入方程,25/m^2-16/(9-m^2)=1,
m^4-50m^2+225=0,
m^2=45(不合題意,>9),m^2=5,m=√5,
n^2=9-5=4,
雙曲線方程為:y^2/5-x^2/4=1.
“m^4-50m^2+225=0",這一步是怎么來(lái)的?