19 the equation (x squared + y squared - 6x + 4y = d) describes a circle. 1. determine the y-coordinate of the center of the circle. ( complete the square) 2. the radius of the circle is 6 units. what is the value of "d" in the given equation?

we have  that

x²-6x+y²+4y=d
Group terms that contain the same variable
(x²-6x)+(y²+4y)=d
Complete the square twice. Remember to balance the equation by adding the same constants to each side
(x²-6x+9)+(y²+4y+4)=d+9+4

Rewrite as perfect squares

(x-3)²+(y+2)²=d+13

the center of a circle is (3,-2)
the radius r²=d+13> 6²=d+13> d=36-13> d=23

the answer is
the Y-coordinate of the center of the circle is -2
d is equal to 23

Part 1:
 For this case we have the following equation:
 x ^ 2 + y ^ 2 - 6x + 4y = d
 By completing squares we have:
 x ^ 2 + y ^ 2 - 6x + 4y + (-6/2) ^ 2 + (4/2) ^ 2 = d + (-6/2) ^ 2 + (4/2) ^ 2
 Rewriting we have:
 x ^ 2 + y ^ 2 - 6x + 4y + (-3) ^ 2 + (2) ^ 2 = d + (-3) ^ 2 + (2) ^ 2
 x ^ 2 + y ^ 2 - 6x + 4y + 9 + 4 = d + 9 + 4
 (x ^ 2 - 6x + 9) + (y ^ 2 + 4y + 4) = d + 13
 (x-3) ^ 2 + (y + 2) ^ 2 = d + 13
 
 The y coordinate of the center of the circle is:
 y = -2
 Part 2:
 For the value of d we have:
 d + 13 = 6
 d = 6 - 13
 d = -7
 
 The value of d is:
 d = -7

Just turn the whole gym into pie