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