Question

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

Answer 1

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:

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

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