Question

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

Solution

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.

SIMILAR QUESTIONS

Q1

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

Q2

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.  

 

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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