Rešenje - Osobine kružnica

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

$$d=2\cdot r$$

r=26

$$d=2\cdot 26$$

$$d=52$$

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

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

r=26

$$c=2\cdot 26\cdot \pi$$

$$c=52\cdot \pi$$

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

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

r=26

$$a={26}^2\cdot \pi$$

$$a=676\cdot \pi$$

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:
$${\left(x+11\right)}^2+{\left(y+15\right)}^2=676$$
$$h=-11$$
$$k=-15$$
Središte $$\left(-11;-15\right)$$

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 $$x$$:

$${\left(x+11\right)}^2+{\left(y+15\right)}^2=676$$

$${\left(x+11\right)}^2+{\left(0+15\right)}^2=676$$

$${\left(x+11\right)}^2+{\left(15\right)}^2=676$$

$${\left(x+11\right)}^2+225=676$$

$${\left(x+11\right)}^2=676-225$$

$${\left(x+11\right)}^2=451$$

$$\sqrt{\left({\left(x+11\right)}^2\right)}=\sqrt{\left(451\right)}$$

$$x+11=\sqrt{\left(451\right)}$$

$$x=\pm \sqrt{\left(451\right)}-11$$

$$x_1=\left(\sqrt{\left(451\right)}-11,0\right),x_2=\left(-\sqrt{\left(451\right)}-11,0\right)$$

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 $$y$$:

$${\left(x+11\right)}^2+{\left(y+15\right)}^2=676$$

$${\left(0+11\right)}^2+{\left(y+15\right)}^2=676$$

$${\left(11\right)}^2+{\left(y+15\right)}^2=676$$

$$121+{\left(y+15\right)}^2=676$$

$${\left(y+15\right)}^2=676-121$$

$${\left(y+15\right)}^2=555$$

$$\sqrt{\left({\left(y+15\right)}^2\right)}=\sqrt{\left(555\right)}$$

$$y+15=\sqrt{\left(555\right)}$$

$$y=\pm \sqrt{\left(555\right)}-15$$

$$y_1=\left(0,\sqrt{\left(555\right)}-15\right),y_2=\left(0,-\sqrt{\left(555\right)}-15\right)$$