Answer :

Given that we need to find the equation of the circle that circumscribes the triangle formed by the lines x = 0, y = 0, and lx + my = 1.



Let us assume A, B, C are the vertices of the triangle.


On solving the lines we get,


A = (0,0)


B =


C =


We have the circle passing through the points A(0,0), B and C.


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


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


Substituting A(0,0) in (1), we get,


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


c = 0 ..... (2)


Substituting B in (1), we get,




cm2 + 2mb + 1 = 0 ..... - (3)


Substituting C in (1), we get,




cl2 + 2al + 1 = 0 ..... (4)


On solving (2), (3) and (4) we get,



Substituting these values in (1), we get




The equation of the circle is .


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