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

Question

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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Aubrey 1 week 2021-09-11T09:27:35+00:00 1 Answer 0

Answers ( )

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    2021-09-11T09:29:05+00:00

    Answer:

    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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