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Thread: Curves + Tangents

  1. #1
    Senior Member
    Jul 2008

    Exclamation Curves + Tangents

    Hi guys

    I've been doing some revision for my yearlies and I'm stuck on these questions:

    1) Find the values of m for which the curves y = mx and y = abs(sinx) have only one common point.

    2) Show that, if the line y = mx + c is a tangent to the curve 4x^2 + 3y^2 = 12, then c^2 = 3m^2 + 4.

    3) The curves with equations y = 4/x + 2 and y = ax^2 + bx + c have the following properties:
    1. there is a common point where x = 2
    2. there is a common tangent where x =2
    3. both curves pass through the point (1,6)
    Find the values of a, b and c.

    Could you please help me out?

    Thanx a lot.
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  2. #2
    MHF Contributor chisigma's Avatar
    Mar 2009
    near Piacenza (Italy)
    The question nr 1 is very easy if you design the graph of the functions $\displaystyle y=mx$ and $\displaystyle y=|\sin x|$. The two curves have only one common point in $\displaystyle x=0$ if $\displaystyle |m|\ge 1$...

    A little more interesting would be the research of the values of $\displaystyle m$ for which $\displaystyle y=mx$ and $\displaystyle y= \sin x$ have only one common point ...

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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