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Find the Equation of the Circle Which Circumscribes the Triangle Formed by the Lines X = 0, Y = 0 and Lx + My = 1. - Mathematics

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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Exercise 24.3 | Q 11 | Page 38
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