Answer 1

Putting x = 0 in 3x + 4y = 12:
y = 3
Putting y = 0 in 3x + 4y = 12:
x = 4
Thus, the line 3x + 4y = 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

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