Question

二次曲线x^2/4+y^2/m=1,当m€[-2,-1)时该直线的离心率e的取值范围是

Answer 1

m∈[-2,-1],则是双曲线.

a^2=4,b^2=-m.c^2=a^2+b^2=4-m

e=c/a

c^2=e^2*a^2

4-m=4e^2

e^2=(4-m)/4.

又5