Find The Equation Of The Circum Circle Of The Quadrilateral Formed By The Four Lines ax + by ± c = 0 And bx – ay ± c = 0.

Find the centre and radius of the circle 

             2x² + 2y² = 3x – 5y + 7

Find the equation of the circle whose centre is the point of intersection of the lines 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 and passes through the origin.

Find the equation of the circle concentric with the circle x² + y² – 8x + 6y– 5 = 0 and passing through the point (–2, –7).

A circle has radius 3 units and its centre lies on the line y = x – 1. Find the equation of the circle if it passes through (7, 3).

Find the area of an equilateral triangle inscribed in the circle

                       x² + y² + 2gx + 2fy + c = 0     

Find the parametric form of the equation of the circle

                               x² + y² + px + py = 0

If the parametric of form of a circle is given by

(i) x = – 4 + 5 cos θ and y = – 3 + 5 sin θ  

(ii) x = a cos α + b sin α and y = a sin α – b cos α

Find its Cartesian form.

Find the equation if the circle the end points of whose diameter are the centres of the circle x² + y² + 6x – 14y = 1 and x² + y² – 4x + 10y = 2.

The sides of a square are x = 2, x = 3, y = 1and y = 2. Find the equation of the circle drawn on the diagonals of the square as its diameter.

The abscissa of two points A and B are the roots of the equation x² + 2ax – b² = 0 and their ordinates are the roots of the equation x² + 2px –q² = 0. Find the equation and the radius of the circle with AB as diameter.