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

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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