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find the inverse of the point 5 10 with respect to a circle with centre at a point 3,4 of diameter 12 units |
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Answer» 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 Learn More: The inverse of (1,3) with the respect of the circle x2+y2-4x-6y+9=0 find the equation of circle which passed through origin and cuts off ... Equation of the circle which is such that the lengths of the TANGENTS ... |
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