Find The Locus Of Pole Of The Line lx + my + n = 0 With Respect To The Circle Which Touches y-axis At The Origin.

If two tangents are drawn from a point on the circle x² + y² = 25 to the circle x² + y² = 25. Then find the angle between the tangents.

Find the equation of diameter of the circle x² + y² + 2gx + 2fy + c = 0 which corresponds o the chord ax + by + λ = 0. 

Examine if the two circle x² + y² – 2x – 4y = 0 and x² + y² – 8y – 4 = 0 touch each other externally or internally. Also the pointed contact.

Find the equation of the circle passing through (1, 1) and the point of intersection of circles.

         x² + y² + 13x – 3y = 0 and 2x² + 2y² + 4x – 7y – 25 = 0

Find the equation of circle passing through the point of intersection of the circle x² + y² – 6x + 2y + 4 = 0 and x² + y² + 2x – 4y – 6 = 0 and whose centre lies on the line y = x.

Find the equation of the circle passing through the points of intersection of the circles x² + y² – 2x – 4y – 4 = 0 and x² + y² – 10x – 12y – 40 = 0.

Find the equation of circle through points of intersection of circle x² + y²– 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x + 2y = 0.

Find the angle between the circles. S = x² + y² – 4x + 6y + 11 = 0 and 

Find the equation of the system of circles coaxial with the circles.

              x² + y² + 4x + 2y + 1 = 0, x² + y² – 2x + 6y – 6 = 0

Also find the equation of that particular circle whose centre lies on radical axis.

Find the circle whose diameter is the common chord of the circles

x² + y² + 2x + 3y + 1 = 0 and x² + y² + 4x + 3y + 2 = 0 

S ≡ x² + y² + 2x + 3y + 1 = 0 S’ ≡ x² + y² + 4x + 3y + 2 = 0