Q. 7 C5.0( 1 Vote )

Find the equation of the circle which circumscribes the triangle formed by the lines:

x + y = 2, 3x - 4y = 6 and x - y = 0

Answer :

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



x + y = 2


3x - 4y = 6


x - y = 0


On solving these lines we get the intersection points A(2,0), B(- 6, - 6), 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 (2,0) in (1), we get


22 + 02 + 2a(2) + 2b(0) + c = 0


4 + 4a + c = 0


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


Substituting (- 6, - 6) in (1), we get


(- 6)2 + (- 6)2 + 2a(- 6) + 2b(- 6) + c = 0


36 + 36 - 12a - 12b + c = 0


12a + 12b - c - 72 = 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


a = 2, b = 3,c = - 12.


Substituting these values in (1), we get


x2 + y2 + 2(2)x + 2(3)y - 12 = 0


x2 + y2 + 4x + 6y - 12 = 0


The equation of the circle is x2 + y2 + 4x + 6y - 12 = 0.


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