Question

双曲线的两条渐近线方程为x y=0和x-y=0,直线2x-y-3=0与双曲线交于a,b两点,|ab|=根号5,求双曲线方

Answer 1

设双曲线为x^2-y^2=k,①

把y=2x-3代入①,整理得3x^2-12x+9+k=0,

△=144-12（9+k)=12(3-k),

|AB|=[(√△）/3]√5=√5,

△=9,3-k=3/4,k=9/4.

∴双曲线为x^2-y^2=9/4.