已知圆C与直线x+y-2根号2=0相切于点A(根号2,根号2),且圆心在直线y=-2x上

2025-05-08 23:27:07
推荐回答(1个)
回答1:

圆心C在过切点A与直线x+y-√2=0垂直的直线L上
x+y-√2=0斜率K=-1,L斜率KL
KL*K=-1,KL=1,
L:y=x
C为y=x和y=-2x交点C(0,0)
半径R^2=(√2)^2+(√2)^2=4
C方程x^2+y^2=4
2)
AB:Y=2X-√2,AD=2X+3√2
带入圆x^2+y^2=4
B(-√2/5,-7√2/5),D(7√2/5,√2/5)
KBD=1