Question

过点(2,-3)且与椭圆9x^2+4y^2=36有共同焦点,求该椭圆方程

Answer 1

x^2/4+y^2/9=1

a^2=9,b^2=4

所以c^2=5

所以假设所求的是x^2/m^2+y^2/n^2=1

则n^2-m^2=5

x^2/m^2+y^2/(m^2+5)=1

过点(2,-3)

4/m^2+9/(m^2+5)=1

9m^2+4(m^2+5)=m^2(m^2+5)

m^2=10,m^2=-2(舍去)

x^2/10+y^2/15=1