Question

Wyznacz srodek i promien okregu o podanym rownaniu

a)x2+y2=144

b)(x+7)2+(y−3)2=8

c)x2+y2+2x=0

d)x2+y2−4x+6y+9=0

e) x2+y2−10x−8y−8=0

f)x2+y2+x−y+1=0

Answer 1

a)

x^2 + y^2 = 144

( x - 0)^2 + ( y - 0)^2 = 12^2

Odp.

S = (0; 0) oraz  r = 12

===========================

b)

(x+7)^2 + ( y -3)^2 = 8

S = ( -7; 3)  oraz  r^2 = 8  = 4*2  =>  r = 2 p(2)

Odp.

S = ( -7; 3)  oraz  r = 2 p(2)

==============================

c)

x^2 + y^2 + 2x = 0

(x + 1)^2 -1 + ( y - 0)^2 = 0

(x+1)^2 + ( y - 0)^2 = 1

Odp.

S = ( -1; 0)   oraz  r = 1

=====================

d)

x^2 + y^2 - 4x + 6y + 9 = 0

(x -2)^2 -4 + ( y + 3)^2 - 9 + 9 = 0

( x- 2)^2 + ( y + 3)^2 = 4

Odp.

S = ( 2 ; -3)  oraz  r = 2

===========================

e)

x^2 + y^2 -10 x - 8y - 8 = 0

(x - 5)^2 - 25 + ( y - 4)^2  - 16 - 8 = 0

(x -5)^2 + ( y - 4)^2 = 49

Odp.

S = ( 5; 4)  oraz  r = 7

======================

f)

x^2 + y^2 + x - y + 1 = 0

( x + 1/2)^2 - 1/4  + (y - 1/2)^2  -1/4  + 1 = 0

(x + 1/2)^2 + ( y - 1/2)^2 = - 1/2

To nie jest równanie okręgu rzeczywistego

lub jest błąd w danych.

==========================================