Find The Equation Of A Circle Which Touches The x-axis And The Line 4x – 3y+ 4 = 0. Its Centre Lies In The Third Quadrant And Lies On The Line x – y – 1 = 0.

If the origin be one limiting point of a system of co-axial circles of whichx² + y² + 3x + 4y + 25 = 0 is a member, find the other limiting point.

Find the radical axis of co-axial system of circles whose limiting points are (–1, 2) and (2, 3).

Find the equation of the circle which passes through the origin and belongs to the co-axial of circles whose limiting points are (1, 2) and (4, 3).

Find the equation of the image of the circle x² + y² + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.

Find the area of the triangle formed by the tangents drawn from the point (4, 6) to the circle x² + y² = 25 and their chord of contact. Also find the length of chord of contact.

Find the lengths of external and internal common tangents to two circlesx² + y² + 14x – 4y + 28 = 0 and x² + y² – 14x + 4y – 28 = 0.      

Find the lengths of common tangents of the circles x² + y² = 6x and x² +y² + 2x = 0.  

Find the equation of the circle circumscribing the triangle formed by the lines:

         x + y = 6, 2x + y = 4 and x + 2y = 5,

Without finding the vertices of the triangle.

Find the equation of the circle circumscribing the quadrilateral formed by the lines in order are 5x + 3y – 9 = 0, x – 3y = 0, 2x – y = 0, x + 4y – 2 = 0 without finding the vertices of quadrilateral.

Find the equations of the circle which passes through the origin and cut off chords of length a from each of the lines y = x and y = –x.