解答 - 圆的性质

直径$$\left(d\right)$$等于半径的两倍：
$$d=2·r$$

$$d=2\cdot r$$

r=3

$$d=2\cdot 3$$

$$d=6$$

周长$$\left(c\right)$$等于半径的两倍乘以π：
$$c=2·r·\pi$$

$$c=2\cdot r\cdot \pi$$

r=3

$$c=2\cdot 3\cdot \pi$$

$$c=6\cdot \pi$$

面积$$\left(a\right)$$等于半径的平方乘以π：
$$a=r^2·\pi$$

$$a=r^2\cdot \pi$$

r=3

$$a=3^2\cdot \pi$$

$$a=9\cdot \pi$$

圆心的坐标通常由$$h$$和$$k$$在圆的标准形式方程中表示：
$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
在方程中确定$$h$$和$$k$$：
$${\left(x-1\right)}^2+{\left(y-1\right)}^2=9$$
$$h=1$$
$$k=1$$
Center $$\left(1;1\right)$$

为了找到$$x$$的交点，将$$0$$代入$$y$$到圆的标准形式方程
$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
并为$$x$$解二次方程式：

$${\left(x-1\right)}^2+{\left(y-1\right)}^2=9$$

$${\left(x-1\right)}^2+{\left(0-1\right)}^2=9$$

$${\left(x-1\right)}^2+{\left(-1\right)}^2=9$$

$${\left(x-1\right)}^2+1=9$$

$${\left(x-1\right)}^2=9-1$$

$${\left(x-1\right)}^2=8$$

$$\sqrt{\left({\left(x-1\right)}^2\right)}=\sqrt{\left(8\right)}$$

$$x-1=\sqrt{\left(8\right)}$$

$$x=\pm \sqrt{\left(8\right)}+1$$

$$x_1=\left(\sqrt{\left(8\right)}+1,0\right),x_2=\left(-\sqrt{\left(8\right)}+1,0\right)$$

求解$$y$$截距，将$$0$$代入圆方程标准形式$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
然后解该二次方程获得$$y$$：

$${\left(x-1\right)}^2+{\left(y-1\right)}^2=9$$

$${\left(0-1\right)}^2+{\left(y-1\right)}^2=9$$

$${\left(-1\right)}^2+{\left(y-1\right)}^2=9$$

$$1+{\left(y-1\right)}^2=9$$

$${\left(y-1\right)}^2=9-1$$

$${\left(y-1\right)}^2=8$$

$$\sqrt{\left({\left(y-1\right)}^2\right)}=\sqrt{\left(8\right)}$$

$$y-1=\sqrt{\left(8\right)}$$

$$y=\pm \sqrt{\left(8\right)}+1$$

$$y_1=\left(0,\sqrt{\left(8\right)}+1\right),y_2=\left(0,-\sqrt{\left(8\right)}+1\right)$$

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