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Math Help - line and circle equations

  1. #1
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    line and circle equations




    the points A and B lie on a circle with centre P, as shown in figure 3.
    the point A has coordinates (1,-2) and the midpoint M of AB has coordinates (3,1).
    The line l passes through the points M and P.

    a)find an equation for l.

    Given that the x-coordinate of P is 6,

    b) use your answer to part (a) to show that the y-coordinate of P is -1
    (i could do this bit if i had the equation)

    c) find an equation for the circle
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  2. #2
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    Quote Originally Posted by kls7162 View Post

    the points A and B lie on a circle with centre P, as shown in figure 3.
    the point A has coordinates (1,-2) and the midpoint M of AB has coordinates (3,1).
    The line l passes through the points M and P.

    a)find an equation for l.

    ...
    The line l is perpendicular to AM and passes through M.

    1. Calculate the slope of AM:

    m_{AM} = \frac{1-(-2)}{3-1}=\frac32

    Therefore the slope of the line l is m_l = -\frac23

    Now use point-slope-formula to get the equation of l:

    y-1 = -\frac23 (x-3)~\implies~ \boxed{y = -\frac23 x +3}

    I'll leave the rest for you.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Circles

    for par A use slope point form y-f(x_0)=m(x-x_0) and to get m just use m=\frac{\Delta{y}}{\Delta{x}}
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