Question

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

Solution

Correct option is

Equation of the circle be x2 + y2 = a2A(x1y1), B(x2y2­)

Since they are conjugate x1x2 + y1y2 = a2   

   

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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.  

 

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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