Let AB be A Chord Of The Circle x2 + y2 = a2 subtending A Right Angle At The Centre. Then The Locus Of The Centroid Of The Triangle PAB as Pmoves On The Circle 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 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:

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:

The triangle PQR is inscribed in the circle x² + y² = 25. If Q and R have co-ordinates (3, 4) and (–4, 3) respectively than ∠QPR is equal  to

The lines joining the origin to the points of intersection of the line 4x + 3y = 24 with the circle (x – 3)² + (y – 4)² = 25 are