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    Could someone please help me with this. Am I supposed to find the turning points and find the distance between them and the origin...

    Thanks,

    Varun
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    turning points?
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    it's a circle and you can draw it to see how it works. Shortest and longest distance can see from the line joining O with the centre of the circle
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    maximum and minimum points...
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    answer is 2...
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    ah ok (x - 3) ^ 2 + (y + 4 ) ^ 2 = 49 ?

    a center 3,-4 with a radius 7 or something , havent done much of C2 yet
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    mmm.
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    2 and 12...right?
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    x²+y²-6x+8y=24
    (x-3)²+(y+4)²-9-16=24
    (x-3)²+(y+4)² = 49

    Length of radius = 7 units
    Centre of circle = (3,-4)

    Line passing through (3,-4) and origin (0,0)
    gradient = (3-0)/(-4-0) = -3/4

    y - 0 = -3/4(x-0)
    y = -3x/4

    Now sub this equation into x²+y²-6x+8y=24
    x²+(-3x/4)²-6x+8(-3x/4) = 24
    x²+9x²/16-6x-24x/4=24
    x²+3x²/4-6x-6x=24
    x²+3x²/4-12x=24
    4x²+3x²-48x=96
    7x²-48x-96=0
    (7x+12)(x-8) = 0
    x = -12/7 or 8

    y = -3(-12/7)/4 = 36/28 = 9/7
    y = -3(8)/4 = -24/4 = -6

    (-12/7,9/7),(8,-6)
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    shortest distance: r ( radius) - ( 3^2 +4^2)^(1/2) =7-5=2
    greatest distance: 5 + 7 = 12
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Updated: November 18, 2005

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