The longest chord of the circumcircle of the triangle made by x -axis, y -axis and 4x + 3y = 24 is:

The longest chord means diameter. The given lines make a right-angled triangle. The circumcircle will touch all three vertices of the triangle. Since there is a right angle at a vertex, the side opposite to that will be the diameter. The line is 4x + 3y = 24. This line touches the x-axis at(0, 8) and the y-axis at (6,0). The distance between the points is the diameter.

The distance between the two points is $$\sqrt{\ 8^2+6^2}=10$$