If on a given base `B C ,` a triangle is described such that the sum of the tangents of the base angles is `m ,` then prove that the locus of the opposite vertex `A` is a parabola.

If on a given base BC[B(0,0) and C(2,0)], a triangle is described such that the sum of the base angles is 4, then the equation of the locus of the opposite vertex A is parabola whose directrix is y=k. The value of k is _________ .

If on a given base,a triangle be described such that the sum of the tangents of the base angles is a constant,then the locus of the vertex is: (A) a circle (Bi a parabola (C) an ellipse (D) a hyperbola

If the base of a triangle and the ratio of tangent of half of base angles are given,then identify the locus of the opposite vertex.

Having given the bases and the sum of the areas of a number of triangles which have a common vertex,show that the locus of the vertex is a straight line.

Given the base of a triangle and the sum of its sides,prove that the locus of the centre of its incircle is an ellipse.

Given the base of a triangle and the ratio of the tangent of half the base angles.Show that the vertex moves on a hyperbola whose foci are the extremities of a diameter

In triangle ABC, base BC is fixed. Then prove that the locus of vertex A such that tan B+tan C= Constant is parabola.

The ends of hypotenuse of a right angled triangle are (a,0),(-a,0) then the locus of third vertex is

If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.

If a triangle is formed by any three tangents of the parabola y^(2)=4ax, two of whose vertices lie on the parabola x^(2)=4by, then find the locus of the third vertex