A Circle Of Radius 2 Lies In The First Quadrant And Touches Both The Axes Of Co-ordinates. Find The Equation Of The Circle With Centre At (6, 5) And Touching The Above Circle Externally.

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Question

A circle of radius 2 lies in the first quadrant and touches both the axes of co-ordinates. Find the equation of the circle with centre at (6, 5) and touching the above circle externally.

Solution

Correct option is

x2 + y2 – 12x – 10 y + 52

 

Given, AC = 2 units

and        A ≡ (2, 2), B ≡ (6, 5)

since       AC + CB = AB

∴            2 + CB = 5

∴                  CB = 3 

Hence equation of required circle with centre at (6, 5) and radius 3 is  

                  (x – 6)2 + (y – 5)2 = 32

or            x2 + y2 – 12x – 10 y + 52 = 0

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