## Question

If two circles, each of radius 5 units, touch each other at (1, 2) and the equation of their common tangent is 4*x* + 3*y* = 10, then equation of the circle, a portion of which lies in all the quadrants is

### Solution

*x*^{2} + *y*^{2} + 6*x* + 2*y* – 15 = 0

Centre of the circle are given by

⇒ Centre are (5, 5) and (–3, –1) and the circles are *x*^{2} + *y*^{2} – 10*x* – 10*y*+ 25 = 0 and *x*^{2} + *y*^{2} + 6*x* + 2*y* – 15 = 0

I^{st} circle lies in the first quadrant as it touches both the axes and centre is also in this quadrant.

#### SIMILAR QUESTIONS

If two lines *a*_{1}*x* + *b*_{1}*y* + *c*_{1} = 0 and *a*_{2}*x* + *b*_{2}*y* + *c*_{2} = 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 *r*^{2}, 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 (*a*, *b*) and the coordinates axis is a

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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 *x*^{2} + *y*^{2} – 6*x* – 4*y* + 9 = 0 bisects the circumference of the circle *x*^{2} + *y*^{2} – (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 *r *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