Final answer:
The locus of the vertex is an elliptical curve.
The Correct Option is; b. A parabola.
Step-by-step explanation:
An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci is constant. In this case, the sum of the tangents of the base angles is constant. Therefore, the locus of the vertex is an elliptical curve, which is option c. An ellipse.
If, on a given base, a triangle is described such that the sum of the tangents of the base angles is a constant, then the locus of the vertex is a: