Question

在平面直角坐标系xOy中,曲线y=x^2 - 6x+1与坐标轴的交点都在圆C上?⑴求圆C的方程?⑵若圆C与直线...

Answer 1

(1)设圆x^2+y^2+Dx+Ey+F=0

x=0,y=1有1+E+F=0

y=0,x^2 - 6x+1=0与x^2+Dx+F=0是同方程,有D=-6,F=1,E=-2

(2)将y=x+a代入圆得2x^2+(2a-8)x+a^2-2a+1+0.OA⊥OB则x1*x2+y1*y2=0

2x1*x2+a(x1+x2)+a^2=0得a=-1