The Lengths Of The Tangents From Two Points A and B to A Circle Are l and l’ respectively. If The Points Are Conjugate With Respect To The Circle, Then (AB)2 Is Equal To

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

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

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

The circle x² + y² – 6x – 4y + 9 = 0 bisects the circumference of the circle x² + y² – (λ + 4)x – (λ + 2)y + (5λ + 3) = 0 if λ is equal to

The locus of the middle points of the chords of the circle of radius r which subtend an angle π/4 at any point on the circumference of the circle is a concentric circle with radius equal to

If two circles, each of radius 5 units, touch each other at (1, 2) and the equation of their common tangent is 4x + 3y = 10, then equation of the circle, a portion of which lies in all the quadrants is