A Square Is Formed By Following Two Pairs Of Straight Lines y2 – 14y + 45 = 0 And x2 – 8x + 12 = 0. A Circle Is Inscribed In It. The Centre Of The Circle 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

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

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

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² – 3ax + dy – 1= 0 intersect in two distinct points P and Q then the line

5x + by – a = 0 passes through P and Q for:  

The intercept on the line y = x by the circle x² + y² – 2x = 0 is AB. Equation of the circle on AB as diameter is:

Let PQ and RS be tangents at the extremities the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals