If Two Circles Which Pass Through The Points (0, a) And (0, –a) Cut Each Other Orthogonally And Touch The Straight Line  Y = mx + c, Then

An equation of the circle through (1, 1) and the points of intersection ofx² + y² + 13x – 3y = 0 and 2x² + 2y² + 4x – 7y – 25 = 0 is   

The abscissae of two points A and B are the roots of the equation x² + 2ax – b² = 0, and their ordinates are the roots of the equation x² + 2px –q² = 0. The radius of the circle with AB as diameter is  

The locus of the point of intersection of the tangent to the circle x = r cos θ, y = r sin θ at points whose parametric angles differ by

 is 

The locus of a point which moves such that the tangents from it to the two circles x² + y² – 5x – 3 = 0 and 3x² + 3y² + 2x + 4y – 6 = 0 are equal is 

If the two circles x² + y² + 2gx + 2fy = 0 and x² + y² + 2g₁x + 2f₁y = 0 touch each other, then

If two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 cut the coordinates axes in concyclic points, then 

The locus of the point which moves in a plane so that the sum of the squares of its distances from the lines ax + by + c = 0 and

bx – ay + d = 0 is r², is a circle of radius.  

The locus of the centre of the circle passing through the origin O and the points of intersection of any line through (a, b) and the coordinates axis is a

Four distinct point (1, 0), (0, 1), (0, 0) and (t, t) are concyclic for

The coordinates of two point P and Q are (2, 3) and (3, 2) respectively. Circles are described on OP and OQ as diameters; O being the origin, then length of the common chord is