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.

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

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 coordinate of that vertex.

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.

The sides of a rectangle are x and y, respectively. Find the rule for finding the perimeter of the rectangle.

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

The base of a triangle passes through a fixed point (f,g) and its sides are respectively bisected at right angles by the lines y+x=0 and y - 9x = 0 Determine the locus of its vertex.

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

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.

Let a line x/a+y/b=1 intersects the x-axis at A and y-axis at B resapectively. A line parallel to it is drawn to intersect the axes in P and Q respectively. The extermities of the lines are joined transversely. If the locus of point of intersection of the line joining them is x/a=cy/b, then c is equal to

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio