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 PQRS has its side PQ paralle to the line y=mx and vertices P,Q and S are on the straight 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

The end points P and Q of a rod PQ having length 8 unit slide along the lines y = 2 and x = 4 respectively. Find the equation of the locus of the mid point of the rod.

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.

If the lines y = 3x + 1 " and " 2y = x + 3 are equally inclined to the line y = mx + 4 ,find the value of m.

If the straight line (x)/(a) + (y)/(b) = 1 is parallel to the line 4x + 3y = 6 and passes through the point of intersection of the lines 2x - y - 1 = 0 and 3x - 4y + 6 = 0 ,find the values of a and b .

A rectangle has two opposite vertices at the points (1, 2) and (5,5). If the other vertices lie on the line x=3 , find the other vertices of the rectangle.

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , 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

The line y=(3x)/4 meets the lines x-y+1=0 and 2x-y=5 at A and B respectively. Find Coordinates of P on y=(3x)/4 such that PA*PB=25.

A circle of radius r passes through the origin and intersects the x-axis and y-axis at P and Q respectively. Show that the equation to the locus of the foot of the perpendicular drawn form the origin upon the line segment bar (PQ) is (x^(2)+y^(2))^(3)=4r^(2)x^(2)y^(2) .