Find The Angle Between The Circles

If two tangents are drawn from a point on the circle x² + y² = 50 to the circle x² + y² = 25 then find the angle between the tangents.

Find the equation of the diameter of the circle

x² + y² + 2gx + 2fy + c = 0 which corresponds to the chord ax = by + d= 0.

Find the locus of the pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

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

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

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

Find the equation of the circle passing through the point of intersection of the circles x² + y² – 6x + 2y + 4 = 0, x² + y² + 2x – 4y – 6 = 0 and with its centre 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 and whose radius is 4.

Find the equation of the circle through points of intersection of the circlex² + y² – 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x+ 2y = 0.

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.

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).