Solusi - Sifat-sifat lingkaran

Diameter $$\left(d\right)$$ sama dengan dua kali jari-jari:

$$d=2\cdot r$$

r=21,213203435596427

$$d=2\cdot 21,213203435596427$$

$$d=42,42640687119285$$

Keliling $$\left(c\right)$$ sama dengan dua kali jari-jari dikali π:

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

r=21,213203435596427

$$c=2\cdot 21,213203435596427\cdot \pi$$

$$c=42,42640687119285\cdot \pi$$

Luas $$\left(a\right)$$ sama dengan kuadrat jari-jari dikali π:

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

r=21,213203435596427

$$a=21,{213203435596427}^2\cdot \pi$$

$$a=450\cdot \pi$$

Koordinat pusat lingkaran biasanya, tetapi tidak selalu, diwakili oleh $$h$$ dan $$k$$ dalam persamaan bentuk umum lingkaran: $${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
Tentukan $$h$$ dan $$k$$ dalam persamaan:
$$a^2+b^2=450$$
$$h=0$$
$$k=0$$
Pusat $$\left(0;0\right)$$

To find the $$x$$ -intercept(s), substitute $$0$$ for $$y$$ in the circle's standard form equation
$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
and solve the quadratic equation for $$x$$:

$${\left(a+0\right)}^2+{\left(b+0\right)}^2=450$$

$${\left(a+0\right)}^2+{\left(0+0\right)}^2=450$$

$${\left(a+0\right)}^2+{\left(-0\right)}^2=450$$

$${\left(a+0\right)}^2+0=450$$

$${\left(a+0\right)}^2=450-0$$

$${\left(a+0\right)}^2=450$$

$$\sqrt{\left({\left(a+0\right)}^2\right)}=\sqrt{\left(450\right)}$$

$$a+0=\sqrt{\left(450\right)}$$

$$a=\pm \sqrt{\left(450\right)}-0$$

$$a_1=\left(\sqrt{\left(450\right)}-0,0\right),a_2=\left(-\sqrt{\left(450\right)}-0,0\right)$$

Untuk menentukan perpotongan sumbu $$y$$, substitusikan $$x$$ dengan $$0$$ dalam persamaan bentuk standar lingkaran $${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$ dan pecahkan soal persamaan kuadrat untuk $$y$$:

$${\left(a+0\right)}^2+{\left(b+0\right)}^2=450$$

$${\left(0+0\right)}^2+{\left(b+0\right)}^2=450$$

$${\left(-0\right)}^2+{\left(b+0\right)}^2=450$$

$$0+{\left(b+0\right)}^2=450$$

$${\left(b+0\right)}^2=450-0$$

$${\left(b+0\right)}^2=450$$

$$\sqrt{\left({\left(b+0\right)}^2\right)}=\sqrt{\left(450\right)}$$

$$b+0=\sqrt{\left(450\right)}$$

$$b=\pm \sqrt{\left(450\right)}-0$$

$$b_1=\left(0,\sqrt{\left(450\right)}-0\right),b_2=\left(0,-\sqrt{\left(450\right)}-0\right)$$