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 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.

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.

Given the base BC of the triangle ABC and if angleC-angleB=k, a constant, show that the locus of the vertex A is a hyperbola.

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 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 base of a triangle is 80cm and one of the base angles is 60^(@) .If the sum of the lenghts of the other two sides is 90cm,then the length of the shortest side is

Statement 1 : Given the base B C of the triangle and the radius ratio of the excircle opposite to the angles Ba n dCdot Then the locus of the vertex A is a hyperbola. Statement 2 : |S P-S P|=2a , where Sa n dS ' are the two foci 2a is the length of the transvers axis, and P is any point on the hyperbola.

The base of a triangle is divided into three equal parts. If t_1, t_2,t_3 are the tangents of the angles subtended by these parts at the opposite vertex, prove that (1/(t_1)+1/(t_2))(1/(t_2)+1/(t_3))=4(1+1/(t2 2))dot