Question

已知圆C关于y轴对称,过抛物线yx^2=4的焦点,且被直线y=x分成两段弧长之...

Answer 1

抛物线x^2=4y的焦点为F(0,1).设圆心C(0,c),因圆被直线y=x分成两段弧长之比为1:2,故

|c|/√2=|CF|/2=|c-1|/2,

平分,化简得c^2+2c-1=0,c=-1土√2,

∴圆C：x^2+(y+1-√2)^2=6-4√2,或x^2+(y+1+√2)^2=6+4√2.