已知圆(x-1)的平方+y的平方;=1求与直线(1)斜率为3的切线方程(2)x+y-1=0平行的切线

题目

已知圆(x-1)的平方+y的平方;=1求与直线(1)斜率为3的切线方程(2)x+y-1=0平行的切线

答案

1.设直线为y = 3x + b,3x -y + b = 0
圆心C(1,0),半径r = 1
C与3x -y + b = 0的距离d = |3 + b|/√(3²+1²) = |3+b|/√10 = r = 1
b+3 = ±√10
b = ±√10 - 3
y = 3x ±√10 - 3
2.x + y - 1 = 0
y = 1 - x
斜率为-1
设直线为y = -x + b,x + y - b = 0
C与x + y - b = 0的距离d = |1 + 0 - b|/√(1²+1²) = |b-1|/√2 = r = 1
b - 1 = ±√2
b = 1 ±√2
y = -x + 1 ±√2