Question

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

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 $x^2-4x+y^2-3y=0$.