Find the equation of the circle passing through the origin and the points where the line 3*x* + 4*y* = 12 meets the axes of coordinates.

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#### Solution

Putting *x* = 0 in 3x + 4y = 12:*y* = 3

Putting *y* = 0 in 3x + 4y = 12:*x* = 4

Thus, the line 3*x* + 4*y* = 12 meets the axes of coordinates at points *A* (0, 3) and *B* (4, 0).

The equation of the circle with *AB* as the diameter is

\[\left( x - 0 \right)\left( x - 4 \right) + \left( y - 3 \right)\left( y - 0 \right) = 0\] or \[x^2 - 4x + y^2 - 3y = 0\]

Hence, the required equation is

\[x^2 - 4x + y^2 - 3y = 0\]

Concept: Circle - Standard Equation of a Circle

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