Question

Napisz rownanie okregu o srednicy AB

a) A=(−7,3) B=(1,3)

b)A=(2,17) B=(−8,−7)

c) A=(−4,0) B=(6,−8)

d) A=(2,4) B=(−1,3)

Answer 1

a)  A = ( -7; 3)  , B = ( 1;3)

Mamy

S - środek odcinka AB

S = ( (-7 +1)/2 ; (3 +3)/2 ) = (-3 ; 3)

r^2 = I AS I^2 = ( - 3 -(-7))^2 + (3 -3)^2 = 4^2  + 0^2 = 16

Odp.

(x +3)^2 + (y - 3)^2 = 16

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b)  A = (2 ; 17) ,  B = (-8; - 7)

S = ( ( 2 +(-8))/2; (17 - 7)/2 ) = ( -3; 5)

r^2 = I AS I^2 = (-3 -2)^2 + (5 - 17)^2 = (-5)^2 + (-12)^2 = 25 + 144 = 169

Odp.

( x +3)^2 + ( y - 5)^2 = 169

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c)

A = (-4; 0) ,  B = (6; -8)

S = ( (-4 +6)/2 ; (0 -8)/2 ) = ( 1; -4)

r^2 = I AS I^2 = (1 -(-4))^2 + (-4 -0)^2 = 5^2 + (-4)^2 = 25 + 16 = 41

Odp.

( x -1)^2 + ( y + 4)^2 = 41

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d)

A= (2; 4) , B = (-1 ; 3)

S = ( (2 -1)/2 ; (4+3)/2 ) = ( 1/2 ;  7/2)

r^2 = I AS I^2 = ( 1/2 - 2)^2 + (7/2 - 4 )^2 = (-3/2)^2 + ( -1/2)^2 =

= 9/4 + 1/4 = 10/4 = 5/2  = 2,5

Odp.

( x - 0,5)^2 + ( y - 3,5)^2 = 2,5

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