How do you describe the translation of circle #(x - 1)2 + (y - 4)2 = 25# that results in an image whose equation is #(x + 1)2 + (y - 5)2 = 25#?

1 Answer
Mar 23, 2016

Answer:

#((-2),(1)) #

Explanation:

Compare the given equations to the standard equation.

#(x - a)^2 + (y - b)^2 = r^2#

where (a,b) are the coords of centre and r , is the radius.

so #(x-1)^2 + (y-4)^2 = 25 " has centre (1,4)and r =5"#

and #(x+1)^2 + (y-5)^2 = 25" has centre (-1,5) and r = 5 "#

Under a translation the circle retains it's shape, but position is changed.
Just need to consider how the centres have changed.

that is : (1,4) → (-1,5) and as a translation #((-2),(1))#