If two circles intersect at two points , then prove that their centres lie on the perpendicular bisector of the common chord.

The perpendicular from the centre of a circle to a chord

The point of intersection of the asymptotes with the directrices lie on

If two lines intersect each other then the number of common points they have

If two circles touching both the axes intersect at two points P and Q where P=(3,1) then PQ=

Let S = 0, S' = 0 be two circle intersecting at two distinct points and L_1 be their common chord, L_2 is the line joing their centres and L_3 is the radical axis. Then

If four points be taken on a retangular hyperola such that the chords joining any two points is perpendicular to the chord joining the other two, and if alpha, beta, gamma and delta be the inclinations to either asymptote oof the straight lines joining these points to the centre prove that tan alpha tan beta tan gamma tan delta=1

If two circles touching both the axes are passing through (2,3) then length of their common chord is

Show that the points of intersection of the perpendicular tangents to an ellipse lies on a circle.

A is a point on either of two line y+sqrt3absx=2 " at a distance of " 4/sqrt3 units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are