A rectangle PQRS has its side PQ parallel to the line y = mx and vertices P,Q and S on the lines y = a , x = b and `x = -b` respectively . Find the locus of the vertex R .

42.A rectangle ABCD has its side AB parallel to the line y=x and vertices A,B and D lie on y=1,x=2 and x=-2 respectively.If locus of vertex C is ax +y= b then find the value of a +b:

A rectangle ABCD has its side AB parallel to line y=x, and vertices A,B and D lie on y=1,x=2, and x=-2, respectively.The locus of vertex C is x=5 (b) x-y=5y=5 (d) x+y=5

The image of P(a,b) on the line y=-x is Q and the image of Q on the line y=x

Let the line (x)/(a)+(y)/(b)=1 cuts the x and y axes at A and B respectively.Now a line parallel to the given line cuts the coordinate axis at P and Q and points P and Q are joined to B and A respectively.The locus of intersection of the joning lines is

A rhombus has two of its sides parallel to the lines y=2x+3 and y=7x+2 . If the diagonals cut at (1, 2) and one vertex is on the y-axis, find the possible values of the ordinate of that vertex.

A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to the line y = x. If the parameters of the points P & Q on the parabola are p & q respectively, show that p + q = 2. Also show that the locus of the point of intersection of the normals at P & Q is 2x - y = 12.

From a variable point R on the line y = 2x + 3 tangents are drawn to the parabola y^(2)=4ax touch it at P and Q point. Find the locus of the centroid of the triangle PQR.

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P(h,k) with the lines y=x and x+y=2 is 4h^(2). Find the locus of the point P.