Find The Equation Of The Circle Which Touches The Circle X2 + y2 – 6x + 6y + 17 = 0 Externally And To Which The Lines X2 – 3xy – 3x + 9y = 0 Are Normals.

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 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.

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.

Determine the radius of the circle, two of whose tangents are the lines 2x+ 3y – 9 = 0 and 4x + 6y + 19 = 0.

Find the equation of a circle which passes through the point

(2, 0) and whose centre is the limit of the point of intersection of the lines 3x + 5y = 1and (2 + c)x + 5c²y = 1as c → 1.