find the inverse of the point 5 10 with respect to a circle with centre at a point 3,4 of diameter 12 units
Answers
Given : circle with the centre at point (3,4) of diameter 12 units
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 = diameter/2 = 12/2 = 6
Point (5 , 10) hence x = 5 , y = 10
α= r² / ((5 - 3)² + (10 - 4)² ) = 6² /40 = 36/40 = 9/10
α(x−h)+h = (9 /10) (5 - 3) + 3 = 24/5
α(y−k)+k = (9 /10) (10 - 4) + 4 = 47/5
(24/5 , 47/5 ) is inverse of point (5,10) with respect to a circle with the center at the point (3,4) of diameter 12 units
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