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Math Help - Coordinate geometry questions.

  1. #1
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    Coordinate geometry questions.

    I have a few more questions that are giving me a hard time...

    1
    What is the equation of the perpendicular bisector of the line between the points (2,2) an (6,6)?


    2
    What is the equation of a parabola with vertex (0,0) and focus (0,4)

    3
    Given that the equation of a circle is x^2+y^2-10x+4y+13=0,
    find it's center and it's radius.
    Last edited by mr fantastic; February 6th 2010 at 03:23 AM. Reason: Changed post title
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  2. #2
    MHF Contributor
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    Quote Originally Posted by NitroKnight View Post
    I have a few more questions that are giving me a hard time...

    1
    What is the equation of the perpendicular bisector of the line between the points (2,2) an (6,6)?


    2
    What is the equation of a parabola with vertex (0,0) and focus (0,4)

    3
    Given that the equation of a circle is x^2+y^2-10x+4y+13=0,
    find it's center and it's radius.
    hi

    (1) first of all , get the midpoint which is (4,4) , then find the line perpendicular which passes through the midpoint . The gradient of this line would be 1 so the gradient of the line perpendicular to this line = -1 ,

    y-4=-1(x-4)

    y=-x+8

    (2) Focus , F=(0,4) so we know that the parabola is in the form of x^2=4ay , vertex is 0 so the equation would be x^2=16y .

    (3) The general equation is given by

    x^2+y^2+2gx+2fy+c=0 where the radius would be (-g,-f) and the radius = \sqrt{g^2+f^2-c}

    so for this question , 2g=-10 , g=-5 and 2f=4 , f=2

    centre =(5,-2) and radius =\sqrt{(-5)^2+(2)^2-13}=4
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