Question

已知椭圆准线为x=25/4且短轴长为6 求椭圆方程

Answer 1

设椭圆方程为：x^2/a^2+y^2/b^2=1,

a>b,椭圆准线为x=a^2/c=25/4,

a^2=25c/4,

2b=6,

b=3,

a^2-c^2=b^2=9,

25c/4-c^2=9,

4c^2-25c+36=0,

(4c-9)(c-4)=0,

c=9/4,或c=4,

a^2=c^2+b^2=225/16,

或a^2=16+9=25,

∴椭圆方程为：x^2/25+y^2/9=1,

或16x^2/225+y^2/9=1.