Solusi - Sifat-sifat lingkaran

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

$$d=2\cdot r$$

r=12

$$d=2\cdot 12$$

$$d=24$$

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

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

r=12

$$c=2\cdot 12\cdot \pi$$

$$c=24\cdot \pi$$

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

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

r=12

$$a={12}^2\cdot \pi$$

$$a=144\cdot \pi$$

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:
$${\left(x-15\right)}^2+{\left(y+8\right)}^2=144$$
$$h=15$$
$$k=-8$$
Pusat $$\left(15;-8\right)$$

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 $$x$$:

$${\left(x-15\right)}^2+{\left(y+8\right)}^2=144$$

$${\left(x-15\right)}^2+{\left(0+8\right)}^2=144$$

$${\left(x-15\right)}^2+{\left(8\right)}^2=144$$

$${\left(x-15\right)}^2+64=144$$

$${\left(x-15\right)}^2=144-64$$

$${\left(x-15\right)}^2=80$$

$$\sqrt{\left({\left(x-15\right)}^2\right)}=\sqrt{\left(80\right)}$$

$$x-15=\sqrt{\left(80\right)}$$

$$x=\pm \sqrt{\left(80\right)}+15$$

$$x_1=\left(\sqrt{\left(80\right)}+15,0\right),x_2=\left(-\sqrt{\left(80\right)}+15,0\right)$$

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 $$y$$:

$${\left(x-15\right)}^2+{\left(y+8\right)}^2=144$$

$${\left(0-15\right)}^2+{\left(y+8\right)}^2=144$$

$${\left(-15\right)}^2+{\left(y+8\right)}^2=144$$

$$225+{\left(y+8\right)}^2=144$$

$${\left(y+8\right)}^2=144-225$$

$${\left(y+8\right)}^2=-81$$

$$\sqrt{\left({\left(y+8\right)}^2\right)}=\sqrt{\left(-81\right)}$$

$$y+8=\sqrt{\left(-81\right)}$$

$$y=\pm \sqrt{\left(-81\right)}-8$$

Tidak ada perpotongan sumbu y