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Math Help - Intersect points

  1. #1
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    Intersect points

    I was given this question: Find the tangent through point (1,-1) of y^2 = x^3 -2x + 2. After some time i found out that this is (x-3)/2. But the b) part of the question was: the curves intersect at another point, find this? And i couldnt because setting both equations equal to each other gives me 1,-1 again..? Thank you!
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  2. #2
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    Re: Intersect points

    If y^2= x^3- 2x+ 2, then 2yy'= 3x^2- 2 so that at (1, -1), -2y'= 1 and y'= -1/2. No, (x- 3)/2 is incorrect because that has slope 1/2, not -1/2.

    Yes, one solution is (1, -1) again but that will be a quadratic equation so there may be another solution.
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  3. #3
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    Re: Intersect points

    Intersect points-curve-intersecting-point.png
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  4. #4
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    Re: Intersect points

    Your first question makes perfect sense. But the second is completely mysterious to me. What curves (plural)? The answer above is one interpretation - namely, find a second point where the tangent line intersects the curve. By the way, there are several good free or inexpensive graphing programs available, Geogebra and Graph, for example. A little time spent "checking your work" with such a program is far faster than online help. I rapidly created the following:
    Intersect points-mhftangents.png
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  5. #5
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    Re: Intersect points

    The second curve is the straight line.
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