A Variable Circle Passes Through A Fixed Point A(p, q) And Touches The x-axis. The Locus Of The Other End Of The Diameter Through A is:

The length of the longest ray drawn from the point (4, 3) to the circle x²+ y² + 16x + 18y + 1 = 0 is equal to

1:- The chords in which the circle C cuts the members of the family S of circles through A and B are con-current at  

2:- Equations of the member of the family S which bisects the circumference of C is

3:- If O is the origin and P is the centre of C, then the difference of the squares of the lengths of the tangents from A and B to the circle C is equal to

If the two (x – 1)² + (y – 3)² = r² and x² + y² – 8x + 2y + 8 = 0 intersect in two distinct points, then

The distance between the chords of contact of the tangent to the circle x² + y² + 2gx + 2fy + c = 0 from the origin and the point (g, f) is

The angle between the tangents drawn from the origin to the circle (x – 7)² + (y + 1)² = 25 is

A square is inscribed in the circle x² + y² – 2x + 4y + 3 = 0. Its sides are parallel to the co-ordinates axes. Then one vertex of the square is

If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49π square units, then the equation of the circle is:

A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is: