Mrs. Culland is finding the center of a circle whose equation is x2 + y2 + 6x - 4y – 3 = 0 by completing the square. Her
work is shown.
x2 + y2 + 6x + 4y - 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (12 + 4y) = 3
(x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4
Which completes the work correctly?
(x - 3)2 + ( - 2)= 42, so the center is (3,2).
(x + 3)2 + (y + 2)2 = 42, so the center is (3, 2).
(x - 3)2 + (x - 2)2 = 42, so the center is (-3,-2).
(x + 3)2 + (y + 2)2 = 42, so the center is (-3, -2).

centre of circle (h,k) is (-3,-2)

Option D is Correct.

Step-by-step explanation:

The centre of circle can be found from the equation as:

So, the steps then by Mrs Culland are:

The next step will be:

I assume there is some calculating mistake in the given options. Instead of 42 there should be 16, according to solution shown above.

The general equation of circle is

In our case:

h= -3 and k= -2, so the centre of circle (h,k) is (-3,-2)

Option D is Correct.

D (x+3)²+(y+2)²=4², so the center is (-3, -2).

Step-by-step explanation:

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

the answer is c)8

step-by-step explanaction: