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Math Help - General Equation of a Circle and Standard form.

  1. #1
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    General Equation of a Circle and Standard form.

    distance formula
    standard form (x-h)^2 + (y-k)^2=r^2
    General form x^2+y^2+ax+by+c=0

    Find Center(h,k) find radius of each circle graph its cirlces

    21. 2(x-3)^2 +2y^2=8
    divide all by 2

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

    Center=(3,0)
    r=2
    xintercepts {5,1}

    31. 2x^2 +2y^2 minus 12x +8y minus 24=0
    all i know is minus 24, complete the square, factor


    Find standard equation
    37. Center (2,3) tangent to x axis
    (x-2)^2 + (y-3)^2 =9

    How did they get 9?
    How does tangent to x axos give me radius of 9?


    41. center (-1,3) tangent to line y=2

    (x+1)^2 + (y-3)^2 =2

    How they get radius of 2?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: General Equation of a Circle and Standard form.

    Quote Originally Posted by Melcarthus View Post
    21. 2(x-3)^2 +2y^2=8
    divide all by 2

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

    Center=(3,0)
    r=2
    xintercepts {5,1}
    Right.

    Quote Originally Posted by Melcarthus View Post
    31. 2x^2 +2y^2 minus 12x +8y minus 24=0
    all i know is minus 24, complete the square, factor
    I would start by dividing thorugh by 2. Then complete the squares:

    x^2 - 6x + 9 +y^2 +4y + 4 = 12 + 9 + 4
    (x-3)^2 + (y+2)^2 = 5^2

    Quote Originally Posted by Melcarthus View Post
    37. Center (2,3) tangent to x axis
    (x-2)^2 + (y-3)^2 =9

    How did they get 9?
    How does tangent to x axos give me radius of 9?
    Given that the circle is tangent to the x axis, the distance from the center to the x-axis is equal to the radius of the circle. The y-coordinate of the center is 3, so that's the radius. Remember that the right jand side is the square of the radius, and 3^2 = 9.

    Quote Originally Posted by Melcarthus View Post
    41. center (-1,3) tangent to line y=2

    (x+1)^2 + (y-3)^2 =2

    How they get radius of 2?
    I think this is in error. The distance from the center at (-1,3) to the line y=2 is 1, so the right hand side should be 1, not 2.
    Last edited by ebaines; December 18th 2012 at 01:25 PM.
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