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Math Help - Parabola - find the equation

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    Parabola - find the equation

    Find the equation of the line tangent to y^2=-16x and parallel to x+y=1.

    Please help me with this or just give me an idea on how to answer this problem... Thanks!
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    Quote Originally Posted by lance View Post
    Find the equation of the line tangent to y^2=-16x and parallel to x+y=1.

    Please help me with this or just give me an idea on how to answer this problem... Thanks!
    If the line is parallel to x + y = 1, then its gradient is 1. (Why?)


    You want the equation of the tangent that has the same gradient.

    So y^2 = -16x

    \frac{d}{dx}(y^2) = \frac{d}{dx}(-16x)

    2y\,\frac{dy}{dx} = -16

    \frac{dy}{dx} = -\frac{8}{y}.


    So when the gradient is 1...

    -\frac{8}{y} = 1

    -\frac{y}{8} = 1

    y = -8.


    When y = -8 we have (-8)^2 = -16x

    64 = -16x

    x = -4.


    So we have the gradient = 1 and a coordinate (-4, -8) that lies on the tangent.

    Put this information into y = mx + c, solve for the unknown c, and then you will have the equation of the tangent.
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