Question

Circle a is defined as (x+5)^2 + (y+6)^2 + 16, and circle b is defined as (x+3)^2+(y+2)^2 =9. Which transformation of circle a shows that circle b is similar?

Answer 1

Step-by-step explanation:D

Answer 2

We should use the following transformation:
`(x', y') = (x+2, y + 4)` (Translation of circle A to the center of the circle B)

Explanation:

We should apply a translation prior to determine if both circles are similar. If we translate the circle A to the center of the circle B. The translation needed is the vectorial distance between both centers:

`T(x,y) = B(x,y)-A(x,y)` (1)

Where:

`T(x,y)` - Translation vector.

`A(x,y)` - Location of the center of the circle A.

`B(x,y)` - Location of the center of the circle B.

If we know that
`A(x,y) = (-5,-6)` and
`B(x,y) = (-3,-2)`, then the translation vector is:

`T(x,y) = (-3,-2)-(-5,-6)`

`T(x,y) = (2,4)`

We should use the following transformation:
`(x', y') = (x+2, y + 4)` (Translation of circle A to the center of the circle B)