Question

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) + (y2 + 4y) = 3 (x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4 Which completes the work correctly? (x – 3)2 + (y – 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 + (y – 2)2 = 42, so the center is (–3, –2). (x + 3)2 + (y + 2)2 = 42, so the center is (–3, –2).

Answer 1

The correct answer is:

(x + 3)^2 + (y + 2)^2 = 4^2, so the center is (–3, –2)

Further explanation:

The given equation of circle is:

$x^2+y^2+6x+4y-3 = 0$

In order to complete the square the terms have to be combined first

$x^2+y^2+6x+4y = 3\\x^2+6x+y^2+4y=3\\(x^2+6x)+(y^2+4y) = 3$

9 and 4 will be added to both sides of the equation to complete the square

$(x^2+6x+9)+(y^2+4y+4) = 3+9+4\\(x^2+6x+9)+(y^2+4y+4) = 16$

The next step completes the work

$(x+3)^2+(y+2)^2 = (4)^2$

Comparing with the standard form of circle

$(x-h)^2 + (y-k)^2 = r^2\\x - h = x+3\\h=-3\\y-k = y+2\\k = -2$

As the centre is (h,k), the centre of given circle will be:

(-3,-2)

Hence the correct answer is:

(x + 3)^2 + (y + 2)^2 = 4^2, so the center is (–3, –2)

Keywords: Circle, Equation of Circle

Learn more about equations of circles at:

• brainly.com/question/3055705
• brainly.com/question/3333996
• brainly.com/question/3456442

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