Q:

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?

Accepted Solution

A:
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