Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #2 20130607 03:48:07
Re: Conicshi {7/3}, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20130609 21:52:31
Re: Conicshi {7/3} You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #7 20130609 22:30:31
Re: ConicsFound a link it doesn't use algebrahttp://xahlee.info/SpecialPlaneCurves_d … ction.html [the link doesn't prove theta is constant for any point ] Last edited by {7/3} (20130609 22:33:33) There are 10 kinds of people in the world,people who understand binary and people who don't. #8 20130610 03:17:40
Re: Conicshi {7/3} The following properties can be deduced immediately: If F'F is extended in both directions there will be a point, A, on this line that lies on the curve. Construct a second line, the perpendicular bisector of F'F. Let these two lines be the x axis and y axis respectively. Let F and F' have coordinates (s,0) and (s,0) respectively. If P (x,y) is a point on the curve then it is easy using symmetry to see that (x,y) (x,y) and (x,y) are also on the curve. Let A be the point (a,0) and let B (on the curve) be the point (o,b) A is on the curve so F'A + AF = constant = (a + s) + (a  s) = 2a. So the constant is 2a. let e < 1 be such that b = a(1  e) then Let MD be the line where D is on the x axis and M is the point with the same y coordinate as P. I think that is the preliminaries dealt with. Now I'm going to work out the equation of this curve. From the basic property: Hold onto your hats. This is where it gets hairy!! Cancelling spree follows but so divide by a^2b^2 I think I need a break now ..... back later to finish off the eccentricity bit Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #12 20130619 03:06:52
Re: ConicsSorry for not being clear,c is distance of foci from center.if i assume a^2+b^2=c^2 i can derive the equation but how do i prove a^2+b^2=c^2? Last edited by {7/3} (20130619 03:10:53) There are 10 kinds of people in the world,people who understand binary and people who don't. #13 20130619 16:59:58
Re: Conicshi {7/3} That should enable you to introduce c. Is that your starting point? Then, how are you defining b ? I think you want e > 0 Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #14 20130619 19:05:57
Re: ConicsI define a as the 1/2 of the distance of the two vertace and b as 1/2 of the line segment that is perpendicular to major axis,passes through center and its length corresponds to height of asymptotes over/under a vertex Last edited by {7/3} (20130619 19:09:59) There are 10 kinds of people in the world,people who understand binary and people who don't. #15 20130619 20:42:04
Re: Conicshi {7/3} I'm assuming you can use that in the same way we used the for an ellipse. From that you can show that the constant is 2a. The focus and directrix properties will follow once you have the equation, but you might as well define some things in preparation. eg. Define c to be ae for some e > 1 Start with (1) and substitute in what we have ( a, c etc) Simplify as before. Define b^2 = a^2(e^2  1) and the right equation should arrive after some work. (I haven't tried it yet ) This definition for b is actually equivalent to the formula you wanted to prove but the asymptote properties will come as a consequence rather than as a starting point. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #18 20130621 22:49:29
Re: ConicsArhh. Now that is a question. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #21 20130622 01:18:38
Re: ConicsI like the definition that asymptote is tangent to the curve at infinity. There are 10 kinds of people in the world,people who understand binary and people who don't. #22 20130622 01:25:32
Re: ConicsCheck this http://www3.ul.ie/~rynnet/swconics/HP%27s.htm first property how was it derived??? Last edited by {7/3} (20130622 01:40:31) There are 10 kinds of people in the world,people who understand binary and people who don't. #23 20130622 02:28:12
Re: Conicshi has y = x as its tangent at infinity. Please don't ask me to do so. I've just spent most of the day checking and filing paperwork and now my head is like this Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #25 20130623 11:06:51
Re: ConicsIf i can prove that property,i won't need eccentricity for the equation. Last edited by {7/3} (20130623 11:09:51) There are 10 kinds of people in the world,people who understand binary and people who don't. 