Question

find the inverse of the point (5,10) with respect to a circle with the centre at point (3,4) of its diameter

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Answer 1

Given :   circle with the centre at point (3,4)  

To find :  The inverse of (5,10) with the respect of the given circle

Solution:

inverse of  (x , y)   wrt circle (α(x−h)+h, α(y−k)+k)

α=r²/ ((x−h)²+(y−k)²)

circle with the centre at point (3,4)

h = 3 , k = 4

r = radius is missing here

Point (5 , 10)  hence x = 5  , y = 10

α=  r² / ((5 - 3)² + (10 - 4)² )  =  r² /40

α(x−h)+h  =    (r² /40) (5 - 3) + 3  = r² /20   + 3

α(y−k)+k  =   (r² /40) (10 - 4) + 4  =  3r² /20   + 4

By substituting value of r inverse of the point (5,10) with respect to a circle with the centre at point (3,4) can be found.

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