Question

椭圆的焦点在x轴上,焦距为4/3*根号33,且通过点(2,1),

Answer 1

∵2c=4√33/3,∴c=2√33/3,c²=44/3,b²=a²-44/3,

椭圆的焦点在x轴上,故设椭圆方程为x²/a²+y/(a²-44/3)=1,

将点(2,1)代入方程得4/a²+1/(a²-44/3)=1,

整理得3a^4-59a²+176=0,即(a²-16)(3a²-11)=0,

∴a²=16或a²=11/3(舍去)

∴b²=16-44/3=4/3,

∴椭圆方程是x²/16+3y²/4=1.