The base AB of a triangle is fixed and its vertex C moves such that sin A =k sin B `(kne1)`. Show that the locus of C is a circle whose centre lies on the line AB and whose radius is equal to `(ak)/((1-k^2))`, a being the length of the base AB.

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.

In a triangle ABC with fixed base BC, the vertex A moves such that cos B + cos C = 4 sin^(2) A//2 If a, b and c denote the lengths of the sides of the triangle opposite to the angles A,B and C respectively, then

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

Let A (2,-3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on line 2x + 3y = 1, then the locus of the vertex C is the line :

The equation of the circle with radius 3 units, passing through the point (2, 1) and whose centre lies on the line y + x = 0 can be

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 ,b and c , denote the length of the sides of the triangle opposite to the angles A , B and C , 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

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2,\ 3) and B is (1,\ 4) .

A triangle A B C with fixed base B C , the vertex A moves such that cosB+cosC=4sin^2A/2dot 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

Let the base A B of a triangle A B C be fixed and the vertex C lies on a fixed circle of radius rdot Lines through Aa n dB are drawn to intersect C Ba n dC A , respectively, at Ea n dF such that C E: E B=1:2a n dC F : F A=1:2 . If the point of intersection P of these lines lies on the median through A B for all positions of A B , then the locus of P is a circle of radius r/2 a circle of radius 2r a parabola of latus rectum 4r a rectangular hyperbola

The radius of the circle whose centre is (-4,0) and which cuts the parabola y^(2)=8x at A and B such that the common chord AB subtends a right angle at the vertex of the parabola is equal to