Question

Does \(x^2 + 4xy + y^2 = 1\) form a hyperbola?

Answer 1

@ganeshie8
@zepdrix

Answer 2

You can use wolfram alpha to plot equations. http://www.wolframalpha.com/input/?i=plot+x%5E2+%2B+4xy+%2B+y%5E2+%3D+1 The graph makes it pretty obvious.

Answer 3

My only question was that, the lines seem to approach infiniti as straight lines.

Answer 4

Those are called asymptotes.

Answer 5

But if you look at the graph it looks like a straight line, the asymptotes are straight lines that never touch the hyperbola right?
So we do say it is a hyperbola?

Answer 6

Yes. Beyond the graph, you can also see that it matches the standard form for a conic section that @ganeshie8 posted.

Answer 7

Alright, thank you! ^^