I'm not sure whether this should go on basic algebra or here, but since I'm learning this in college I'm gonna post it here. Ok, I'm in dire need of help with two problems:
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.
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 gonna 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(b^2 * (x^2/a^2 - 1)) which I got from the reduced equation of a hyperbola to y = bx/a + d). I ended up with (b^2 - b)*x^2 + (2dba)*x + (d^2*a^2 + a^2*b^2). Then I supposed B^2 - 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.