The correct answer is: A. Straight line
The locus of reaction of a two hinged semi-circular arch is a straight line. This is because the reaction force at each hinge is always perpendicular to the tangent to the arch at that point. The tangent to the arch at any point is a straight line, so the locus of all these tangents is also a straight line.
The other options are incorrect because they are not straight lines. A parabola is a curved shape that opens upwards or downwards, a circle is a round shape, and a hyperbola is a curved shape that opens outwards in both directions.