Results 1 to 4 of 4

Math Help - Help! Coordinate Geometry

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    14

    Help! Coordinate Geometry

    1. The line y=2x-12 meets the coordinate axes at A and B. The line AB is a diameter of the circle. Find the equation of the circle?

    2. The Points A(7,4) B(8,-7) and C(-4,3) lie on a circle
    a) Show that triangle ABC has a right angle?
    b) Find the equation of the circle?

    3. Show that triangle ABC is isosceles where A(0,5) , B(2,6) and C(3,4)?


    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    Quote Originally Posted by Colin_m View Post
    1. The line y=2x-12 meets the coordinate axes at A and B. The line AB is a diameter of the circle. Find the equation of the circle?
    First find where the line crosses the axes.
    y=2x-12
    Take y=0, then x=6
    Take x=0, then y=-12
    So the points are A(6,0) and B(0,-12).
    |AB| is the diameter of the circle. Then the middle point of |AB| is the center (O), and the length of |OA| or |OB| is the radius.

    O\left (\frac{6+0}{2},\frac{0-12}{2}\right) = O(3,-6)

    |OA| = \sqrt{45}

    The equation of the circle is,
    (x-a)^2+(y-b)^2=r^2

    (x-3)^2+(y+6)^2=45
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Colin_m View Post
    1. The line y=2x-12 meets the coordinate axes at A and B. The line AB is a diameter of the circle. Find the equation of the circle?

    Mr F says: You can get A and B, right? The midpoint of AB is the midpoint of the circle. Half of the length of AB is the radius of the circle. Sub into {\color{red}(x - h)^2 + (y-k)^2 = r^2}.

    2. The Points A(7,4) B(8,-7) and C(-4,3) lie on a circle
    a) Show that triangle ABC has a right angle?
    b) Find the equation of the circle?

    Mr F says: (a) Get the gradient of AB, AC and BC. Which pair of gradients have a product equal to -1? Therefore which pair of line segments are perpendicular?

    (b) There is a circle theorem that says that the angle subtended at the circumference by a diameter is equal to 90 degrees. So have a think about which point the 90 degree is at and therefore which of AB, AC, BC will be a diameter of the circle. Then proceed in the same way as Q1.


    3. Show that triangle ABC is isosceles where A(0,5) , B(2,6) and C(3,4)?

    Mr F says: Calculate the length of each line segment AB, AC and BC. If two of them are the same, then you obviously have an isosceles triangle.

    Thanks
    ..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2007
    Posts
    14
    thanks for the help guys
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Coordinate Geometry
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 16th 2011, 12:06 AM
  2. Coordinate Geometry
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 5th 2010, 05:21 AM
  3. coordinate geometry
    Posted in the Algebra Forum
    Replies: 6
    Last Post: November 25th 2009, 08:28 AM
  4. coordinate geometry
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 24th 2009, 10:35 AM
  5. Coordinate Geometry
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 12th 2008, 05:26 PM

Search Tags


/mathhelpforum @mathhelpforum