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C4 implicit

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    At what points are the tangents to the circle x^2+y^2-6y-8x=0 parallel to the y-axis?

    i differentiated the equation and got:

    2x + 2ydy/dx - 6dy/dx -8

    then my gradient equals this: 8-2x/2y-6

    now what do i do if i equal it to zero one of my co-ordinates my x coordinate will equal 4 and thats not in the answers.

    thanks in advance, kind regards
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    the first part is wrong it 2x+2ydy/dx not minus
    • 114 followers
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    You have an incorrect sign in your differentiated line and forgot = 0

    You are not trying to find when dy/dx = 0

    You are trying to find when the tangent is parallel to the y axis not the x axis
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    You are trying to find when the line is parallel to the y axis so use dx/dy=0

    so (2y-6)/(2x-8)=0

    2y-6=0
    y=3

    When y=3, x^2-8x-9=0
    so (x-9)(x+1)=0

    voila (9,3) and (-1,3)

    Are these right?
    • Thread Starter
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    (Original post by BigBrain)
    You are trying to find when the line is parallel to the y axis so use dx/dy=0

    so (2y-6)/(2x-8)=0

    2y-6=0
    y=3

    When y=3, x^2-8x-9=0
    so (x-9)(x+1)=0

    voila (9,3) and (-1,3)

    Are these right?
    yessss you genuissssss
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    The gradient is undefined when denominator=0

    dy/dx= (2x-8)/(2y-6)=0

    Solve the denominator for 0.

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Updated: April 2, 2012
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