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 rectangle ABCD is inscribed in a circle with a diameter lying along the line 3y =x + 10. If A and B are the points (-6, 7) and (4, 7) respectively, find the area of the rectangle

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

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.

A point P moves on a plane (x)/(a)+(y)/(b)+(z)/(c)=1. A plane through P and perpendicular to OP meets the coordinate axes at A, B and C.If the parallel to the planes x=0,y=0 and z=0, respectively, intersect at Q, find the locus of Q.

One side of a rectangle lies along the line 4x + 7y +5=0. Two of its vertices are (-3, 1) and (1, 1).Find the equations of the other three sides.

Find the value of x such that PQ = QR, where P, Q and R are (6,- 1), (1, 3) and (x, 8) respectively.

The image of P(a,b) on the line y=-x is Q and the image of Q on the line y=x is R . then the midpoint of PR is

Two fixed straight lines X - axis and y = mx are cut by a variable line in the points A(a,0) and B(b,mb) respectively .P and Q are the feet of the perpendiculars drawn from A and B upon the lines y = mx and X - axis ,Show that ,if AB passes through a fixed point (h,k) then PQ will also pass through a fixed point .