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Thread: [ASK] Equation of a Circle

  1. #1
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    [ASK] Equation of a Circle

    find standard eqations of circles that have centers on 4x+3y=8 and are tangent to both the line x+y=-2 and 7x-y=-6

    What I got is $\displaystyle 4a=4\pm3r\sqrt2$ and $\displaystyle b=4\pm r\sqrt2$. Dunno how to continue from here.
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  2. #2
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    Re: [ASK] Equation of a Circle

    the distance from the center $(a,b)$ of such a circle to a given straight line is equal to the radius $r$ of the circle

    Furthermore $4a+3b=8$
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  3. #3
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    Re: [ASK] Equation of a Circle

    Yes, I did that. In fact, that was how I got to the aforementioned $\displaystyle 4a=–4\pm3r\sqrt2$ and $\displaystyle b=4\pm r\sqrt2$.
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    Re: [ASK] Equation of a Circle

    Quote Originally Posted by Monoxdifly View Post
    Yes, I did that. In fact, that was how I got to the aforementioned $\displaystyle 4a=–4\pm3r\sqrt2$ and $\displaystyle b=4\pm r\sqrt2$.
    How did you get those equations? Show your work.

    use $4a+3b=8$ to find $r$

    The problem has two solutions.
    Thanks from topsquark
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  5. #5
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    Re: [ASK] Equation of a Circle

    Quote Originally Posted by Idea View Post
    How did you get those equations? Show your work.
    By substituting 4a + 3b = 8 to the formula $\displaystyle y-b=m(x-a)\pm r\sqrt{1+m^2}$.
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