Solusi - Sifat-sifat lingkaran

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

$$d=2\cdot r$$

r=8,306623862918075

$$d=2\cdot 8,306623862918075$$

$$d=16,61324772583615$$

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

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

r=8,306623862918075

$$c=2\cdot 8,306623862918075\cdot \pi$$

$$c=16,61324772583615\cdot \pi$$

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

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

r=8,306623862918075

$$a=8,{306623862918075}^2\cdot \pi$$

$$a=69\cdot \pi$$

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:
$${\left(x+5\right)}^2+{\left(y+9\right)}^2=69$$
$$h=-5$$
$$k=-9$$
Pusat $$\left(-5;-9\right)$$

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 $$x$$:

$${\left(x+5\right)}^2+{\left(y+9\right)}^2=69$$

$${\left(x+5\right)}^2+{\left(0+9\right)}^2=69$$

$${\left(x+5\right)}^2+{\left(9\right)}^2=69$$

$${\left(x+5\right)}^2+81=69$$

$${\left(x+5\right)}^2=69-81$$

$${\left(x+5\right)}^2=-12$$

$$\sqrt{\left({\left(x+5\right)}^2\right)}=\sqrt{\left(-12\right)}$$

$$x+5=\sqrt{\left(-12\right)}$$

$$x=\pm \sqrt{\left(-12\right)}-5$$

Tidak ada perpotongan sumbu x

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 $$y$$:

$${\left(x+5\right)}^2+{\left(y+9\right)}^2=69$$

$${\left(0+5\right)}^2+{\left(y+9\right)}^2=69$$

$${\left(5\right)}^2+{\left(y+9\right)}^2=69$$

$$25+{\left(y+9\right)}^2=69$$

$${\left(y+9\right)}^2=69-25$$

$${\left(y+9\right)}^2=44$$

$$\sqrt{\left({\left(y+9\right)}^2\right)}=\sqrt{\left(44\right)}$$

$$y+9=\sqrt{\left(44\right)}$$

$$y=\pm \sqrt{\left(44\right)}-9$$

$$y_1=\left(0,\sqrt{\left(44\right)}-9\right),y_2=\left(0,-\sqrt{\left(44\right)}-9\right)$$