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

Answer:

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

Step-by-step 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)

Answer 2

Answer:

Step-by-step explanation:D