Rešenje - Osobine kružnica

Prečnik $$\left(d\right)$$ ima dvostruku vrednost radijusa:

$$d=2\cdot r$$

r=9,899494936611665

$$d=2\cdot 9,899494936611665$$

$$d=19,79898987322333$$

Opseg $$\left(c\right)$$ ima dvostruku vrednost radijusa pomnoženo sa π:

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

r=9,899494936611665

$$c=2\cdot 9,899494936611665\cdot \pi$$

$$c=19,79898987322333\cdot \pi$$

Površina $$\left(a\right)$$ ima vrednost kvadrata radijusa pomnoženo sa π:

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

r=9,899494936611665

$$a=9,{899494936611665}^2\cdot \pi$$

$$a=98\cdot \pi$$

Koordinate središta kružnice se obično, ali ne uvek, prikazuju sa $$h$$ i $$k$$ u standardnoj jednačini kružnice: $${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
Otkrijte $$h$$ i $$k$$ u jednačini:
$${\left(x-3\right)}^2+{\left(y+1\right)}^2=98$$
$$h=3$$
$$k=-1$$
Središte $$\left(3;-1\right)$$

Da biste našli $$x$$ -presek(e), supstitucirajte $$0$$ za $$y$$ u standardnoj formi jednačine kruga
$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
i rešite kvadratnu jednačinu za $$x$$:

$${\left(x-3\right)}^2+{\left(y+1\right)}^2=98$$

$${\left(x-3\right)}^2+{\left(0+1\right)}^2=98$$

$${\left(x-3\right)}^2+{\left(1\right)}^2=98$$

$${\left(x-3\right)}^2+1=98$$

$${\left(x-3\right)}^2=98-1$$

$${\left(x-3\right)}^2=97$$

$$\sqrt{\left({\left(x-3\right)}^2\right)}=\sqrt{\left(97\right)}$$

$$x-3=\sqrt{\left(97\right)}$$

$$x=\pm \sqrt{\left(97\right)}+3$$

$$x_1=\left(\sqrt{\left(97\right)}+3,0\right),x_2=\left(-\sqrt{\left(97\right)}+3,0\right)$$

Da bi se pronašli odsečci na osi $$y$$, zameni $$0$$ za $$x$$ u standardnoj jednačini kružnice $${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$ i reši kvadratnu jednačinu za $$y$$:

$${\left(x-3\right)}^2+{\left(y+1\right)}^2=98$$

$${\left(0-3\right)}^2+{\left(y+1\right)}^2=98$$

$${\left(-3\right)}^2+{\left(y+1\right)}^2=98$$

$$9+{\left(y+1\right)}^2=98$$

$${\left(y+1\right)}^2=98-9$$

$${\left(y+1\right)}^2=89$$

$$\sqrt{\left({\left(y+1\right)}^2\right)}=\sqrt{\left(89\right)}$$

$$y+1=\sqrt{\left(89\right)}$$

$$y=\pm \sqrt{\left(89\right)}-1$$

$$y_1=\left(0,\sqrt{\left(89\right)}-1\right),y_2=\left(0,-\sqrt{\left(89\right)}-1\right)$$