Final answer:
The locus described in the question forms an ellipse, defined by the constant sum of distances from any point on it to the two foci, which in this scenario are represented by the perpendicular axes.
The correct answer is option A ellipse.
Step-by-step explanation:
The locus of a point that divides a line of fixed length moving in such a way that its ends are always on two fixed perpendicular lines is an ellipse.
An ellipse is defined as a closed curve such that the sum of the distances from any point on the curve to two fixed points (foci) is a constant.
In the context of this question, the two perpendicular lines act as the axes, and the moving line segment ensures that the sum of distances from any point that divides the line into portions of length a and b to the axes will remain constant, satisfying the definition of an ellipse.