Find the equation of a circle circumscribing a square ABCD with side l and AB, AD as co-ordinate axes.

Find the equation of the ellipse satisfying the given condition : Axes along co-ordinate axes, passing through (4, 3) and (- 1, 4).

Find the equation of the circle, which is circumscribed about the triangle whose vertices are (-2, 3), (5, 2) and (6, -1).

Find the equation of a line that cuts off equal intercepts on the co-ordinate axes and passes through the point (5, 6).

Find the equation of the ellipse referred to its axes as the axes of co-ordinates : whose major axis =6 and minor axis = 4 .

Find the equation of the ellipse referred to its axes as the axes of co-ordinates : whose major axis = 8 and eccentricity = 1/2 .

Find the equation of the ellipse referred to its axes as the axes of co-ordinates : which passes through the points ( - 2, 1) and eccentricity = sqrt (2/5)

2x-y+4=0 is a diameter of a circle which circumscribes a rectangle ABCD. If the coordinates of A, B are (4, 6) and (1, 9) respectively, find the area of this rectangle ABCD.

Find the equation of the ellipse referred to its axes as the axes of co-ordinates : whose latus-rectum is 5 and eccentricity 2/3 .

Find the equation of the ellipse referred to its axes as the axes of co-ordinates : whose foci are (2, 0), (-2, 0) and latus-rectum is 6.