Find The Equation Of The Tangents To The Circle x2 + y2 = 9, Which Are Perpendicular To The Line 2x + 3y + 7 = 0.

A circle of radius 5 units touches the co-ordinates axes in first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, find its equation in the new position.

Discuss the position of the points (1, 2) and (6, 0) with respect to the circle

                          x² + y² – 4x +2y – 11 = 0.

Find the shortest and largest distance from the point (2, –7) to the circle 

                   x² + y² – 14x – 10y – 151 = 0

Find the points of intersection of the line 2x + 3y = 18 and the circle x² +y² = 25.

Find the length of the intercept on the straight line 4x – 3y – 10 = 0 by the circle x² + y² – 2x + 4y – 20 = 0.

Find the co-ordinates of the middle point of the chord which the circlex² + y² + 4x – 2y – 3 = 0 cuts off the line x – y + 2 = 0.

For what value of λ will the line y = 2x + λ be a tangent to the circle x² +y² = 5?

Find the equation of tangent to the circle x² + y² – 2ax = 0 at the point   

Find the equation of the tangents to the circle x² + y² = 9, which  Are parallel to the line 3x + 4y – 5 = 0

Find the equation of the tangents to the circle x² + y² = 9, which make an angle of 60^o with the x-axis.