已知双曲线的焦距是2倍根号5,一条渐近线平分圆x方加y方减4x加2y=0.求双曲线方程

Question

已知双曲线的焦距是2倍根号5,一条渐近线平分圆x方加y方减4x加2y=0.求双曲线方程

Answer 1

c^2=(2根号5)^2=20x^2+y^2-4x+2y^2=0即x^2-4x+4+y^2+2y+1=0+4+1=5(x-2)^2+(y+1)^2=5平分圆,所以渐近线过圆的圆心（2,-1） b/a=1/2,b=1/2a,b^2=1/4a^2,a^2+b^2=5/4a^2=c^2=20,a^2=16,b^2=c^2-a^2=4所以双曲线方程是x^...