3:- If O is The Origin And P is The Centre Of C, Then The Difference Of The Squares Of The Lengths Of The Tangents From A and B to The Circle C is Equal To

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 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

A point moves such that the sum of the squares of its distances from the sides of a square of side unity is equal to 9. The locus of such a point is a circle

Radical centre of the three circles x² + y² = 9, x² + y² – 2x – 2y = 5, x² + y² + 4x + 6y = 19 lies on the line y = mx if m is equal to

The coordinates of the point on the circle x² + y² – 2x – 4y – 11 = 0 farthest from the origin are 

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0,b). The reflection of O in the line AB is the point

The length of the longest ray drawn from the point (4, 3) to the circle x²+ y² + 16x + 18y + 1 = 0 is equal to

1:- The chords in which the circle C cuts the members of the family S of circles through A and B are con-current at  

2:- Equations of the member of the family S which bisects the circumference of C is

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