Question

Please help me..

Answer 1

Answer: A: (x + 4)² + (y - 5)² = 8

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²     where

• (h, k) is the center of the circle
• r is the radius of the circle

To find the equation of circle A, we need (h, k) and r².

It is given that (h, k) = (-4, 5)

The distance between the center of circles A and B is the radius of circle A.

Let's find the center of circle B by completing the square:

x² - 4x + ____ +  y² + 6y + _____ = 12 + ____ + _____

     ↓                            ↓      

  h = -4/2                    k = 6/2

  h = -2                       k = 3              →  Circle B has center (-2, 3)

Now let's find the distance between the center of circles A and B:

$(r_A)^2=d^2=(x_A-x_B)^2+(y_A-y_B)^2$

                = (-4 - (-2))² + (5 - 3)²

                =     (-2)²     +     2²

                =       4        +     4

                = 8

Now we have the the center (h, k) and the r² for circle A:

(h, k) = (-4, 5) and r² = 8   →    (x + 4)² + (y - 5)² = 8