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 equation of the circle which cuts the circle x² + y² + 5x + 7y – 4 = 0 orthogonally, has its centre on the line x = 2 and passes through the point (4, –1).

Find the equations of the two circles which intersect the circles

        x² + y² – 6y + 1 = 0 and x² + y² – 4y + 1 = 0  

Orthogonally and touch the line 3x + 4y + 5 = 0.   

Find the radical centre of circles x² + y² + 3x + 2y + 1 = 0,

x² + y² – x + 6y + 5 = 0 and x² + y² + 5x – 8y + 15 = 0. Also find the equation of the circle cutting them orthogonally.

Find the radical centre of three circles described on the three sides 4x – 7y + 10 = 0, x + y – 5 = 0 and 7x + 4y – 15 = 0 of a triangle as diameters.

Find the co-ordinates of the limiting points of the system of circles determined by the two circles

  x² + y² + 5x + y + 4 = 0 and x² + y² + 10x – 4y – 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 lengths of external and internal common tangents to two circlesx² + y² + 14x – 4y + 28 = 0 and x² + y² – 14x + 4y – 28 = 0.