The centre of the circle passing through origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line

Explanation

The circle passes through (0,0), (4,0), and (0,6). The points (4,0) and (0,6) form the diameter of the circle because the angle subtended at the origin is a right angle (90^{\circ}). The center of the circle is the midpoint of the diameter, (2, 3). Substituting (2, 3) into the options, we find it satisfies 3(2) - 4(3) + 6 = 6 - 12 + 6 = 0.

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