Results 1 to 4 of 4

Math Help - Circles

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    217

    Circles

    1a) Show that the circle with the equation x^2 + y^2 - 2ax - 2ay + a^2 = 0 touches both the x axis and the y axis.

    b) Hence show that there are exactly two circles passing through the point (2, 4) and just touching the x axis and y axis and give their equations.

    c) State the coordinates of the centres of the two circles and give the radius of each of these circles.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,803
    Thanks
    1692
    Awards
    1
    Quote Originally Posted by Joker37 View Post
    1a) Show that the circle with the equation x^2 + y^2 - 2ax - 2ay + a^2 = 0 touches both the x axis and the y axis.
    b) Hence show that there are exactly two circles passing through the point (2, 4) and just touching the x axis and y axis and give their equations.
    c) State the coordinates of the centres of the two circles and give the radius of each of these circles.
    By completing squares twice that circle is (x-a)^2+(y-a)^2=a^2.
    So it is a circle with center (a,a) and radius r=|a|.
    The point (a,a) is at a distance of |a| from both axes.
    Can you finish?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    217
    Quote Originally Posted by Plato View Post
    Can you finish?
    Sorry, no I cannot. I'm new at this.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,803
    Thanks
    1692
    Awards
    1
    If a circle is tangent to both a axis then the center must be on y=x\text{ or }y=-x.

    For the b part solve for a  (2-a)^2+(4-a)^2=a^2

    Then the radius is |a|.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove that every rigid motion transforms circles into circles
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: February 11th 2010, 06:00 PM
  2. Replies: 2
    Last Post: October 6th 2009, 08:04 AM
  3. going in circles
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: July 23rd 2009, 10:57 AM
  4. Circles!
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 16th 2009, 07:50 PM
  5. circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 16th 2008, 03:40 AM

Search Tags


/mathhelpforum @mathhelpforum