Question

HELP!! PLEASE, 19 POINTS!! The equation (X squared + Y squared - 6x + 4y = d) describes a circle.

1. Determine the Y-coordinate of the center of the circle. (Hint.... Complete the square)
2. The radius of the circle is 6 units. What is the value of "d" in the given equation?

Answer 1

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

Answer 2

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
 Answer:
 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
 Answer:
 The value of d is:
 d = -7