The base `B C` of ` A B C` is fixed and the vertex `A` moves, satisfying the condition `cotB/2+cotC/2=2cotA/2,` then `b+c=a` `b+c=2a` vertex `A` moves along a straight line Vertex `A` moves along an ellipse

BC is the base of the DeltaABC is fixed and the vertex A moves, satisfying the condition cot.(B)/(2) + cot.(C)/(2) = 2 cot.(A)/(2) , then

Base BC of triangle ABC is fixed and opposite vertex A moves in such a way that tan.(B)/(2)tan.(C)/(2) is constant. Prove that locus of vertex A is ellipse.

Statement 1 : In a triangle A B C , if base B C is fixed and the perimeter of the triangle is constant, then vertex A moves on an ellipse. Statement 2 : If the sum of the distances of a point P from two fixed points is constant, then the locus of P is a real ellipse.

a triangle A B C with fixed base B C , the vertex A moves such that cosB+cosC=4sin^2(A/2)dot If a ,ba n dc , denote the length of the sides of the triangle opposite to the angles A , B ,a n dC , respectively, then (a) b+c=4a (b) b+c=2a (c) the locus of point A is an ellipse (d) the locus of point A is a pair of straight lines

A and B are fixed points such that AB=2a. The vertex C of DeltaABC such that cotA+cotB =constant. Then locus of C is

There exists a triangle A B C satisfying the conditions bsinA=a ,A a ,A >pi/2 bsinA > a ,A >a bsinA >pi/2,b=a

In a triangle ABC, if cotA :cotB :cotC = 30: 19 : 6 then the sides a, b, c are

In triangle A B C , if cotA *cotC=1/2a n dcot B* cotC=1/(18), then the value of tanC is

In DeltaABC , if AB = c is fixed, and cos A + cosB + 2 cos C = 2 then the locus of vertex C is

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