Question

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`?

Answer 1

`((-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))`