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

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Solution

The triangle is formed by
$x = 0 \dots (i) y = 0 \dots (i i)$
$l x + m y = 1 \dots (i i i)$
The line (iii) cuts the axis at
$A = (0, \frac{1}{m}), a n d a t B (\frac{1}{l}, 0)$
Now, AB will be the diameter of circle.
$∴$ equation of circle will be,
$(x - \frac{1}{l}) (x - 0) + (y - 0) (y - \frac{1}{m}) = 0 \Rightarrow x^{2} + y^{2} - \frac{x}{l} - \frac{y}{m} = 0$

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