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    Show that the straight line y=x+k meets the curve x^2 +3xy +y^2 =5 in two distinct points for all values of the constant k.
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    (Original post by Tinson)
    Show that the straight line y=x+k meets the curve x^2 +3xy +y^2 =5 in two distinct points for all values of the constant k.
    Tried anything? Any thoughts?
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    (Original post by RDKGames)
    Tried anything? Any thoughts?
    I tried to use simultaneous equations to solve it and I got
    x^2 +xk +1=k^2

    Maybe I don't understand the question asking for. I tried to research my text book but I have no idea.
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    (Original post by Tinson)
    I tried to use simultaneous equations to solve it and I got
    x^2 +xk +1=k^2

    Maybe I don't understand the question asking for. I tried to research my text book but I have no idea.
    Not sure how you got that.

    Imagine if the question said "This line intersects this other curve for all values of k, find the points of intersection". What would your method be to solve that in this scenario? [HINT: Simultaneous eqs. wouldn't be too helpful here, substitution of one eq. into the other perhaps?]
 
 
 
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