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Math Help - [SOLVED] Calculus Word Questions

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    [SOLVED] Calculus Word Questions

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  2. #2
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    Hello, CAIR!

    Find the equation of the tangent to the hyperbola: . \frac{x^2}{16} - \frac{y^2}{9} \:=\:1
    at the point \left(\text{-}5,\tfrac{9}{4}\right) on the curve.
    We have: . 9x^2 - 16y^2 \:=\:144

    Differentiate implicitly: . 18x - 32y\frac{dy}{dx} \:=\:0 \quad\Rightarrow\quad \frac{dy}{dx} \:=\:\frac{9x}{16y}

    At \left(\text{-}5,\tfrac{9}{4}\right),\;\;\frac{dy}{dx} \:=\:\frac{9(\text{-}5)}{16(\frac{9}{4})} \:=\;-\frac{5}{4} . . . slope of the tangent


    The equation of the line through \left(\text{-}5,\tfrac{9}{4}\right) with slope m = \text{-}\tfrac{5}{4} is:

    . . y - \tfrac{9}{4} \;=\;\text{-}\tfrac{5}{4}(x + 5) \quad\Rightarrow\quad\boxed{ y \:=\:\text{-}\tfrac{5}{4}x - 4}

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  3. #3
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    thanks
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