已知圆C:x2+y2+2x-4y+3=01.1.若圆C的切线在X轴Y轴上截距相等,求切线方程 2.从圆C外一点P(x,y)向圆引切线PM,M为切点,O为坐标原点,且有 |PM|=|PO|,求使|PM|最小的点P的坐标.
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![已知圆C:x2+y2+2x-4y+3=01.1.若圆C的切线在X轴Y轴上截距相等,求切线方程 2.从圆C外一点P(x,y)向圆引切线PM,M为切点,O为坐标原点,且有 |PM|=|PO|,求使|PM|最小的点P的坐标.](/uploads/image/z/3706765-61-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%9C%86C%EF%BC%9Ax2%2By2%2B2x-4y%2B3%3D01.1.%E8%8B%A5%E5%9C%86C%E7%9A%84%E5%88%87%E7%BA%BF%E5%9C%A8X%E8%BD%B4Y%E8%BD%B4%E4%B8%8A%E6%88%AA%E8%B7%9D%E7%9B%B8%E7%AD%89%2C%E6%B1%82%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B+2.%E4%BB%8E%E5%9C%86C%E5%A4%96%E4%B8%80%E7%82%B9P%EF%BC%88x%2Cy%EF%BC%89%E5%90%91%E5%9C%86%E5%BC%95%E5%88%87%E7%BA%BFPM%2CM%E4%B8%BA%E5%88%87%E7%82%B9%2CO%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%2C%E4%B8%94%E6%9C%89+%EF%BD%9CPM%EF%BD%9C%3D%EF%BD%9CPO%EF%BD%9C%2C%E6%B1%82%E4%BD%BF%EF%BD%9CPM%EF%BD%9C%E6%9C%80%E5%B0%8F%E7%9A%84%E7%82%B9P%E7%9A%84%E5%9D%90%E6%A0%87.)
已知圆C:x2+y2+2x-4y+3=01.1.若圆C的切线在X轴Y轴上截距相等,求切线方程 2.从圆C外一点P(x,y)向圆引切线PM,M为切点,O为坐标原点,且有 |PM|=|PO|,求使|PM|最小的点P的坐标.
已知圆C:x2+y2+2x-4y+3=01.
1.若圆C的切线在X轴Y轴上截距相等,求切线方程
2.从圆C外一点P(x,y)向圆引切线PM,M为切点,O为坐标原点,且有
|PM|=|PO|,求使|PM|最小的点P的坐标.
已知圆C:x2+y2+2x-4y+3=01.1.若圆C的切线在X轴Y轴上截距相等,求切线方程 2.从圆C外一点P(x,y)向圆引切线PM,M为切点,O为坐标原点,且有 |PM|=|PO|,求使|PM|最小的点P的坐标.
1)
截距相等,斜率k=1或k=-1
a):
k=1,y=x+b
带入圆方程:
2x^2+2(b-1)x+b^2-4b+3=0
△=0
4(b-1)^2-8(b^2-4b+3)=0
b=1或b=5
y=x+1或y=x+5
b):
k=-1,y=-x+b
带入圆方程:
2x^2+2(3-b)x+b^2-4b+3=0
△=0
4(3-b)^2-8(b^2-4b+3)=0
b=3或b=-1
y=-x+3或y=-x-1
所以求切线方程 :
y=x+1或y=x+5或y=-x+3或y=-x-1
2)
P(X,Y)
X^2+Y^2=(X+1)^2+(y-2)^2-2
y=x/2
过圆心(-1,2)
p(2x,x)