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ZeHgS
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Homework Statement
1) A hyperbola goes through the point P(6, 2), and one of its asymptotes is the line r: 2x + 5y = 0. Determine its equation.
2) Prove that a line parallel to one asymptote of a hyperbola interesects it in a single point.
Homework Equations
The Attempt at a Solution
I spent almost two hours on that first problem and tried everything I could, it sounds so fing simple yet I couldn't figure it out. Everything I tried filled up 3-4 pages of my notebook. I must not have understood some basic concept. I'm not going to transcribe everything here because I think it would be pointless, but please believe me when I said I tried it until I couldn't stand it anymore. If you guys could just point me in the right direction...
For the second one I equaled y = sqrt(b2 * (x2/a2 - 1)) which I got from the reduced equation of a hyperbola to y = bx/a + d). I ended up with (b2 - b)*x2 + (2dba)*x + (d2a2 + a2b2). Then I supposed B2 - 4AC should equal 0, which would mean it had only one solution but I just got a really ugly equation and couldn't see why it would equal 0.
Please help I'm almost committing suicide over these two.