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Math Help - for what value of c will the circle with equation x^2+6x+y^2-4y+c=0 have a radius of

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    Red face for what value of c will the circle with equation x^2+6x+y^2-4y+c=0 have a radius of

    for what value of c will the circle with equation x^2+6x+y^2-4y+c=0 have a radius of 4?
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    Re: for what value of c will the circle with equation x^2+6x+y^2-4y+c=0 have a radius

    Quote Originally Posted by vegasgunner View Post
    for what value of c will the circle with equation x^{2}+6x+y^{2}-4y+c=0 have a radius of 4?
    The center of the circle is found by comparison. It is (g=-3,f=2)

    The Radius can be found from an equation of a general formula by R=\sqrt{g^{2}+f^{2}-c}

    Therefore, the reverse can be found by inputting R=4 into 4=\sqrt{g^{2}+f^{2}-c}

    Since we know the center, we input g and f into the above, and get: 4=\sqrt{(-3)^{2}+2^{2}-c}

    Solving for c, we get 16=9+4-c which gives a value for c of c=3
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    Re: for what value of c will the circle with equation x^2+6x+y^2-4y+c=0 have a radius

    Comparison with the general equation of a circle, which is x^{2}+y^{2}+2gx+2fy+c=0 where (-g,-f) is the center of the circle, and the radius is per my previous post. When posting formulas, I think it's neater if you arranged them by powers before variables.
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    Re: for what value of c will the circle with equation x^2+6x+y^2-4y+c=0 have a radius

    Quote Originally Posted by vegasgunner View Post
    for what value of c will the circle with equation x^2+6x+y^2-4y+c=0 have a radius of 4?
    Transform the equation to x^2+6x+9+y^2-4y+4=-c+9+4.

    Now make -c+9+4=16
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