Question

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   

 

Solution

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

                                 

   

SIMILAR QUESTIONS

Q1

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

Q2

If the point (1, 4) lies inside the circle x2 + y2 – 6x – 10y + p = 0 and the circle does not touch or interest the coordinates axes, then

Q3

If the line x cos α + y sin α = p represents the common chord APQB of the circle x2 + y2 = a2 and x2 + y2 = b2 (a > b) as shown in the Fig, then AP is equal to

Q4

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

Q5

If OA and OB are two equal chords of the circle x2 + y2 – 2x + 4y = 0 perpendicular to each other and passing through the origin O, the slopes of OA and OB are the roots of the equation 

Q6

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

Q7

The lengths of the intercepts made by any circle on the coordinates axes are equal if the centre lies on the line (s) represented by

Q8

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

Q9

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

Q10

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.