UC知道圆的问题 会英文的请进！
来源：百度知道 编辑：UC知道 时间：2024/05/27 03:52:05
a)THE vertical line x+2=o 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
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
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
详细解答，请参看下图。
a)
Let the circle be (x-a)² + (y-b)² = r². We want to find a, b and r.
(-2-a)² + (4-b)² = r² --- (1)
a² + b² = r² --- (2)
(7-a)² + (1-b)² = r² --- (3)
Solving Equ.(1) - (3), we have a = 3, b = 4 and r = 5.
Thus the circle is (x-3)² + (y-4)² = 25.
b)
x² + y² - 8x - 4y + 8 = 0 can be rewritten as
x² -