Circle and Syst...

Two circles x² + y² = 6 and x² + y² – 6x + 8 = 0 are given. Then the equation of the circle through their points of intersection and the point (1, 1) is

The locus of the mid-point of a chord of the circle x² + y² = 4 which subtends a right angle at the origin is

If a circle passes through the point (a, b) and cuts the circle x² + y² = k² orthogonally, then the equation of the locus of its centre is

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

The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 154 sq. units. Then the equation of this circle is

The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x² + y² = 9 is

The locus of the centre of a circle, which touches externally the circle x² + y² – 6x – 6y + 14 = 0 and also touches the y-axis, is given by the equation:

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

The angle between a pair of tangents drawn from a point P to the circle x² + y² + 4x – 6y + 9 sin² α + 13 cos² α = 0 is 2α. The equation of the locus of the point P is

If the line y = 7x - 25 meets the circle x² + y² = 25 in the points A, B, then the distance between A and B is