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Math Help - tangent line

  1. #1
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    tangent line

    For each curve, find the equation of the tangent at the given point.

    a) x^2 + y^2 = 13 at (2, -3)

    I got the slope, which is - x/y but I have no clue how to put this into an equation.
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  2. #2
    Senior Member tukeywilliams's Avatar
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    Use point-slope form:  y-y_1 = m(x-x_1)
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  3. #3
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    I have tried that. I get y=2/3 (x) + 5/3 (correct me if I'm wrong), but the answer in the back of my textbook is 2x - 3y - 13 = 0
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  4. #4
    Senior Member tukeywilliams's Avatar
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     y+3 = \frac{2}{3}(x-2)

     y = \frac{2}{3}x - \frac{13}{3}

    So...  3y = 2x - 13

    Or  3y-2x + 13 = 0

    Then  2x-3y-13 = 0
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