The equation of a circle touching the coordinate axes and the line x cos α + y sin α = 2 is x² + y² – 2gx + 2gy + g² = 0, where g is equal to

C₁ and C₂ are circles of unit radii with centres at (0, 0) and (1, 0), respectively. C₃ is a circle of unit radius, which passes through the centres of the circles C₁ and C₂ and has its centre above the x-axis. The equation of the common tangent to C₁ and C₃, which does not pass through C₂, is

A chord of the circle x² + y² – 4x – 6y = 0 passing through the origin subtends an angle tan^–1(7/4) at the point where the circle meets the positive y-axis. The equation of the chord is

If a circle passes through (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is

The length of the common chord of the circles (x – 1)² + (y + 1)² = c² and (x + 1)² + (y – 1)² = c² is

The circles x² + y² – 10x + 16 = 0 and x² + y² = r² intersect each other at two distinct points if

If the locus of a point, which moves so that the line joining the points of contact of the tangents drawn from it to the circle x² + y² = b² touches the circle x² + y² = a², is the circle x² + y² = c², then a, b, c are in

If the point (1, 4) lies inside the circle x² + y² – 6x – 10y + p = 0 and the circle does not touch or intersect the coordinate axes, then

An equation of the chord of a circle x² + y² = a² passing through the point (2, 3), farthest from the centre, is

If two distinct chords, drawn from the point (p, q) on the circle x² + y² = px + qy (where pq ≠ 0), are bisected by the x-axis, then