Q. 7 B5.0( 3 Votes )

Find the eq

Answer :

Given that we need to find the equation of the circle formed by the lines:



2x + y - 3 = 0


x + y - 1 = 0


3x + 2y - 5 = 0


On solving these lines we get the intersection points A(2, - 1), B(3, - 2), C(1,1)


We know that the standard form of the equation of a circle is given by:


x2 + y2 + 2ax + 2by + c = 0 .....(1)


Substituting (2, - 1) in (1), we get


22 + (- 1)2 + 2a(2) + 2b(- 1) + c = 0


4 + 1 + 4a - 2b + c = 0


4a - 2b + c + 5 = 0 ..... (2)


Substituting (3, - 2) in (1), we get


32 + (- 2)2 + 2a(3) + 2b(- 2) + c = 0


9 + 4 + 6a - 4b + c = 0


6a - 4b + c + 13 = 0 ..... (3)


Substituting (1,1) in (1), we get


12 + 12 + 2a(1) + 2b(1) + c = 0


1 + 1 + 2a + 2b + c = 0


2a + 2b + c + 2 = 0 ..... (4)


Solving (2), (3), (4) we get


.


Substituting these values in (1), we get



x2 + y2 - 13x - 5y + 16 = 0


The equation of the circle is x2 + y2 - 13x - 5y + 16 = 0.


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