等轴双曲线的中心在原点,焦点在x轴上,与直线x-2y=0交于A、B两点,且|AB|＝4根号15,求等轴双曲线方程

x^2-y^2=my=x/2代入x^2-x^2/4=m3x^2-4m=0x1+x2=0,x1*x2=-4m/3(x1-x2)^2=(x1+x2)^2-4x1x2=16m/3AB在y=x/2上所以(y1-y2)^2=(x1/2-x2/2)^2=(x1-x2)^2/4=4m/3AB^2=(x1-x2)^2+(y1-y2)^2=16m/3+4m/3=20m/3=(4根号15)^2=240...