If a > 2b > 0 Then The Positive Value Of m for Which  is A Common Tangent To x2 + y2 = b2 and (x – a)2+ y2 = b2 is     

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If a > 2b > 0 then the positive value of m for which  is a common tangent to x2 + y2 = b2 and (x – a)2y2 = b2 is   



Correct option is

 is a tangent to the circle x2 + y2 = b2 for all values of m. If it also touches the circle (x – a)2 + y2 = b2, then the length of the perpendicular from its centre (a, 0) on this line is equal to the radius b of the circle, which gives  


Taking negative value on R.H.S. we get m = 0, so we neglect it.

Taking the positive value on R.H.S. we get





Two rods of lengths a and b slide along the x-axid and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is


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Two points P and Q are taken on the line joining the points A (0, 0) and B (3a, 0) such that AP = PQ = QB. Circles are drawn onAPPQ, and QB as diameters. The locus of the point S, the sum of the squares of the lengths of the tangents from which to the three circles is equal to b2, is


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An equation of the chord of the circle x2 + y2 = a2 passing through the point (2, 3) farthest from the centre is


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A circle touches both the coordinates axes and the line  the coordinates of the centre of the circle can be


If the tangent at the point P on the circle x2 + y2 + 6x + 6y = 2 meets the straight line 5x – 2y + 6 = 0 at a point Q on the y-axis, then the length ofPQ is


Let PQ  and RS be tangents at the extremities of a diameter PR of a circle of radius r. Such that PS and RQ intersect at a point X on the circumference of the circle, then diameter of the circle equals.