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Math Help - Find the equation of the line CB

  1. #1
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    Find the equation of the line CB

    hello, this is my question:

    The point A(3,2) is one end of the diameter AB of a circle. Both A and B lie on the line y=1/3x+1.
    The point C(1,4) lies on the circumference of the circle.

    Fine the equation of CB.

    im not too sure at all how i would do this question so i would require some help please! could you write up step by step what i have to do and explain fully so i can try and understand what is going on?!

    thanks!
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  2. #2
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    Re: Find the equation of the line CB

    Quote Originally Posted by andyboy179 View Post
    .....could you write up step by step what i have to do and
    explain fully so i can try and understand what is going on?!
    That's your teacher's job.
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  3. #3
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    Re: Find the equation of the line CB

    Quote Originally Posted by andyboy179 View Post
    hello, this is my question:

    The point A(3,2) is one end of the diameter AB of a circle. Both A and B lie on the line y=1/3x+1.
    The point C(1,4) lies on the circumference of the circle.

    Fine the equation of CB.

    im not too sure at all how i would do this question so i would require some help please! could you write up step by step what i have to do and explain fully so i can try and understand what is going on?!

    thanks!
    Let's denote center of circle as :

    O(x_O,y_O)

    step 1 .

    Solve following system of equations in order to find center of circle :

    \begin{cases}(x_O-x_A)^2+(y_O-y_A)^2=(x_O-x_C)^2+(y_O-y_C)^2 \\y_O=\frac{1}{3}x_O+1\end{cases}

    step 2 .

    calculate point B :

    x_B=2x_O-x_A

    y_B=2y_O-y_A

    step 3 .

    Write equation of the line CB using equation of the line through two points .

    y-y_C=\frac{y_C-y_B}{x_C-x_B}(x-x_C)
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  4. #4
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    Re: Find the equation of the line CB

    Hi andyboy79,
    The following may be of more help
    1 the perpendicular bisector of AC passes thru the circle center
    2 solution of y=1/3x+1 and ! above gives the center
    3 radius of circle = distance between A and center
    4 determine point B using radius and y=1/3x+1
    5 CB has same slope as 1.Use point slope formular to get equation of CBl
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