Find The Equation Of The Circle Whose Radius Is 5 And Which Touches The Circle                x2 + y2 – 2x – 4y – 20 = 0 At The Point (5, 5).   

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Find the equation of the circle whose radius is 5 and which touches the circle 

              x2 + y2 – 2x – 4y – 20 = 0 at the point (5, 5).   


Correct option is

x2 + y2 – 18x – 16y + 120 = 0


The given circle is x2 + y2 – 2x – 4y – 20 = 0

With centre (1, 2) and radius 


And required circle has radius 5 hence circles touch each other externally. 

Since point of contact is (5, 5).

∴ P is the mid point of C1 and C2, let co-ordinates of centre C2 is (hk) then


∴ Equation of required circle is  

                         (x – 9)2 + (y – 8)2 = 52

⇒                      x2 + y2 – 18x – 16y + 120 = 0




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