已知三點(diǎn)P(5,2),F1(-6,0),F2(6,0),1.求以F1,F2為焦點(diǎn)且過(guò)點(diǎn)P的橢圓的標(biāo)準(zhǔn)方程.
PF1=√125=5√5
PF2=√5
PF1+PF2=2a =6√5
a=3√5 c=6 b^2=a^2-c^2=9
橢圓的標(biāo)準(zhǔn)方程為 x^2/45+y^2/9=1
(2) 關(guān)于直線(xiàn)Y=X的對(duì)稱(chēng)點(diǎn)份額別為P' ,F1' ,F2'
則p'(2,5) F1'(0,-6) F2'(0,6)
P'F1'=√125=5√5
P'F'2=√5
P'F1-P'F'1=4√5 2a=4√5 a=2√5
c=6 a=2√5
b^2=c^2-a^2=36-20=16
過(guò)P'的雙曲線(xiàn)的標(biāo)準(zhǔn)方程 y^2/20-x^2/16=1