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# Algebra and Functions watch

1. 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.
2. (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?
3. (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.
4. (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 , 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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