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31 March, 04:39

Given that the line y=c-2x is tangent to the curve y^2=kx where c and k are non-zero constants, express k in terms of c

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  1. 31 March, 06:55
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    k = - 8c.

    Step-by-step explanation:

    y^2 = kx

    Find the slope of the tangent by differentiating:

    y' 2y = k

    y' = k / 2y = the slope of the tangent.

    The given equation of the tangent is y = - 2x + c so the slope = - 2.

    Therefore k/2y = - 2 so k = - 4y and y = - k/4

    y^2 = kx so k^2/16 = kx giving x = k/16.

    Substituting for x and y in y = - 2x + c:

    -k/4 = - 2 k/16 + c

    -k/4 = - k/8 + c

    c = - k/4 + k/8 = - k/8.

    So - k = 8c

    k = - 8c.
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