1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Equation of circle

  1. Sep 8, 2007 #1
    1. The problem statement, all variables and given/known data

    A circle touches the line y=x at a pont P such that OP = 4*2^1/2 i.e 4root2 , where O is the origin.The circle contains the point (-10,2) in its interior and the length of its chord on the line x+y=0 is 6root2.Determine the equation of the circle.

    The attempt at a solution

    OK as its clear that the chord is perpendicular to the tangent so its part of the normal line and hence the diameter.So the length of the radius of the circle is 3root2.

    Secondly using under-root S1 = length of tangent drawn from (x1,y1) I got c= 32.

    I cant proceed any further.What use is the internal point?
  2. jcsd
  3. Sep 8, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    I would just draw this on graph paper and see if that helps.
  4. Sep 8, 2007 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    The distance from (0,0) to (x,y) is [itex]\sqrt{x^2+ y^2}[/itex]. You are saying that OP= [itex]4\sqrt{2}[/itex] so [itex]x^2+ y^2= 32[/itex]. Since, in addition, the point is on the line y= x, [itex]2x^2= 32[/itex], [itex]x^2= 16[/itex], x= 4. P is the point (4,4). The circle passes through the point (4,4). If you could find the center of the circle, you could use that to find the radius and then write down the equation of the circle.

    Why is it "clear that the chord is perpendicular to the tangent"? the only time a chord is perpendicular to the tangent to the circle is when the chord is a diameter! You appear to use that to conclude that the radius of the circle must be half the length of that chord, but I can see no reason that it should be "clear".
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Equation of circle
  1. Equation of a circle (Replies: 3)

  2. Equation of a circle (Replies: 9)

  3. Equation of a circle (Replies: 11)

  4. Equation of circle (Replies: 6)

  5. Equation of a Circle (Replies: 2)