若椭圆x2/a2+y2/b2=1过点(3,-2),离心率为根号3/3,求a和b的值
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x2/a2+y2/b2=1过点(3,-2),
所以有：9b^2+4a^2=a^2b^2·········································1
离心率为根号3/3 所以有：
c/a=√3/3 即：c^2/a^2=1/3 又：c^2=a^2-b^2
所以可得：a^2=3(a^2-b^2)··········································2
联立1、2解得：a^2=15, b^2=10
所以有：9b^2+4a^2=a^2b^2·········································1
离心率为根号3/3 所以有：
c/a=√3/3 即：c^2/a^2=1/3 又：c^2=a^2-b^2
所以可得：a^2=3(a^2-b^2)··········································2
联立1、2解得：a^2=15, b^2=10
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