Find the equation of the circle which circumscribes the triangle formed by the lines *x* = 0, *y* = 0 and *lx* + *my* = 1.

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#### Solution

The coordinates of *A* and *B* are

\[\left( 0, \frac{1}{m} \right) and \left( \frac{1}{l}, 0 \right)\]

Here, the end points of the diameter of the circumcircle are

*A*and*B*.∴ Required equation of the circle:

\[\left( x - 0 \right)\left( x - \frac{1}{l} \right) + \left( y - \frac{1}{m} \right)\left( y - 0 \right) = 0\]

\[\Rightarrow x^2 - \frac{x}{l} + y^2 - \frac{y}{m} = 0\]

Concept: Circle - Standard Equation of a Circle

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