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


Correct option is

x2 + y2 + 6x + 2y – 15 = 0

Centre of the circle are given by   



⇒ Centre are (5, 5) and (–3, –1) and the circles are x2 + y2 – 10x – 10y+ 25 = 0 and x2 + y2 + 6x + 2y – 15 = 0

Ist circle lies in the first quadrant as it touches both the axes and centre is also in this quadrant.



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


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.  



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


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


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


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


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


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


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


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