Results 1 to 3 of 3

Math Help - Math circles help

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    Trinidad
    Posts
    49

    Math circles help

    question 7 in part A in attached document

    How do i show it is a tangent to the circle?

    what i did was found the centre of the circle to be (1,2)

    then i found the gradient and usuing the princinple that perp. lines product of gradient = -1 found the other gradient to be -1/4

    after plugging the gradient i got C=13/2

    what do i do next?
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,977
    Thanks
    1643

    Re: Math circles help

    There are several different ways to do that.
    1) Solve the equation of the line for y and replace y in the equation of the circle by that expression,, getting a quadratic equation in x. The line is tangent to the circle if and only if the quadratic equation has a double root- if it reduces to (x- a)^2= 0.

    2) By completing the square, find the center of the circle and so find the equation, and then slope of the line from the center of the circle to (2, 6), a radius of the circle. Show that (2, 6) satisfies the equations of both line and circle and show that the line is perpendicular to the radius by showing that the product of their slopes is -1.

    3) Show that x= 2, y= 6 satisfies the equations of both line and circle and show that the slope of the line is equal to the derivative of the equation of the circle at that point.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    914
    Thanks
    27

    Re: Math circles help

    equation of circle put in standard form (x+1)^2 +(y-2)^2 =25
    Center is ?
    Slope of radius from center to (2,6) is ?
    Slope of given line is?
    Are the lines perpendicular
    Does (2,6) satisfy both equations
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. RiDo Circles. Sin & Cos Circles
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: June 14th 2012, 10:34 PM
  2. 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
  3. Replies: 2
    Last Post: October 6th 2009, 08:04 AM
  4. Circles of math
    Posted in the Geometry Forum
    Replies: 3
    Last Post: July 1st 2008, 11:27 AM
  5. Replies: 16
    Last Post: May 3rd 2008, 01:09 PM

Search Tags


/mathhelpforum @mathhelpforum