a)The vertical line x+2=0 touches the circle at point A(-2,4) ,the circle passes though the origin O and the point B(7,1) ,find the equation of the circle.
1)垂线x=-2与圆交于点A(-2,4),圆经过原点及点B(7,1),试写出圆的方程.
线段AO;BO的垂直平分线l1;l2即为圆心.
l1:x-2y+5=0
l2:14x+2y-50=0
O`(3,4)
r=|OO`|=5
圆的方程:(x-3)^2+(y-4)^2=25
b)write down the coordinates of the centre of the x^2+y^2-8x-4y+8=0
the line y=x cuts the circle at points A and B,find the coordinates of M the midpoint of A and B
2)写下圆x^2+y^2-8x-4y+8=0的圆心坐标
(x-4)^2+(y-2)^2=12
圆心坐标(4,2)
直线y=x与圆交于A,B两点,写出线段AB中点M的坐标.
如图:O`M是线段AB的垂直平分线
所以M(3,3)