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Math Help - Finding a tangent line

  1. #1
    Newbie cerberus's Avatar
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    Finding a tangent line

    I'm stuck on this question:

    Find the equations of all lines tangent to y=x^2-4 that pass through the point (5,5).

    I found the derivative of the function (y'=2x), and plugged in 5 to get a slope of 10. Then I put it into the y=mx+b form to solve for "b". I got y=10x-45. But when I graph the original function and the equation of the tangent line, the tangent line isn't... tangent. Help, please!
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    The point (5,5) is not lies on curve y=x^2-4.
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  3. #3
    Newbie cerberus's Avatar
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    Quote Originally Posted by Also sprach Zarathustra View Post
    The point (5,5) is not lies on curve y=x^2-4.
    I understand that. I have no idea how to relate the two...
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    1. Draw the graph y=x^2-4
    2. Draw some tangent line to the graph.
    3. Put the point (5,5) on the line.


    NOW, think how you can get this tangent line equation!



    Hint 1:

    Call the tangent point A(x,y)=A(x,x^2-4). You have also the point (5,5) on this line... so you can find the slope(by two points formula).
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  5. #5
    Newbie cerberus's Avatar
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    Thank you!!
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