Find The Equation Of Normal To The x2 + y2 = 2x which Is Parallel To x + 2y= 3.  

Find the equation of the circle which passes through the origin and makes intercepts of length a and b on axis of x and y respectively.

A circle of radius 2 lies in the first quadrant and touches both the axes of coordinate. Find the equation of circle with centre at (6, 5) and touching the above circle externally.

A circle of radius 5 units touches the coordinates axes in 1^st quadrant. If the circle makes one complete roll on x axis along positive direction of xaxis. Find the equation in new position. 

Discus 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 length of intercept on the S.L. 4x – 3y – 10 = 0 by the circle x²+ y² – 2x + 4y – 20 = 0.

Find the coordinates of the middle point of the chord which the circle x²+ y² + 4x – 2y – 3 = 0 cut off the line x – y + 2 = 0.   

For what values 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 normal at the point (5, 6) to the circle;

x² + y² – 5x + 2y – 48 = 0