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how to graph this circle?

4x^2 + 4y^2 + 40x + 40y + 191 =0

I really need help. I completed the square (I'm pretty sure I did it right) and there is no way to reduce this so I can graph it. HELP PLEASE!

1 Answer

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  • 10 years ago
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    If you have completed the square to get something of the form

    (x-a)² + (y-b)² = r², then the radius is r and the centre is the point (a,b).

    So you have

    4x² + 40x + 4y² + 40y + 191 = 0.

    Let's divide through by 4:

    x² + 10x + y² + 10y + 47.75 = 0

    We can write this as

    x² + 10x + 25 + y² + 10y + 25 + 47.75 - 50 = 0, and noticing the first three terms are (x+5)² and the next three are (y+5)², and tidying up,

    (x+5)² + (y+5)² = 2.25, and noting that 2.25 = 1.5²,

    this is of the desired form with a = -5, b = -5, r = 1.5. So the centre of the circle is the point (-5,-5) and its radius is 1.5.

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