Q. 265.0( 2 Votes )

Find the equation of a circle of radius 5 which is touching another circlex2 + y2 – 2x – 4y – 20 = 0 at (5, 5).

Answer :

x2 - 2x + y2 - 4y – 20 = 0


x2 - 2x + 1 +y2 - 4y +4 – 20 – 5 = 0


(x – 1)2 + (y – 2)2 = 25


(x – 1)2 + (y – 2)2 = 52


Since, the equation of a circle having centre (h,k), having radius as "r" units, is


(x – h)2 + (y – k)2 = r2


Centre = (1, 2)


Point of Intersection = (5, 5)


It intersects the line into 1: 1, as the radius of both the circles is 5 units.


Using Ratio Formula,



Ratio = m1 : m2


Assuming the co-ordinates of the centre of the circle be (p,q)






p + 1 = 10, q + 2 = 10


p = 9 & q = 8


Co-ordinates = (9,8)


Equation is,


(x – h)2 + (y – k)2 = r2


(x – 9)2 + (y – 8)2 = 52


x2 - 18x + 81 + y2 - 16y + 64 = 25


x2 - 18x + y2 - 16y + 145 – 25 = 0


x2 - 18x + y2 - 16y + 120 = 0


Hence, the required equation is x2 - 18x + y2 - 16y + 120 = 0.


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