Ploting general equation of conics

[ahmadriaz]

i have made a program that takes input of Ax^2+By^2+Cxy+Dx+Ey+F=0

it determines the type pf curve and finds all the related elements...now i want to ad the GRAPHS as well...but i can't find a way...i just completed my 12th standard so i don't have enough knowlege...even i can't find related pages on GOOGLE... can u please please guide me how to plote Ax^2+By^2+Cxy+Dx+Ey+F=0

please do help...coz the program means a lot to me...

i think polar form will solve my prob...please guide me
REGARDS
AHMAD

 

[chaoseverlasting]

You are right, if you use parametric equations, you can get a pretty good graph. I assume you're using Turbo C++? If you want, I've done the code already and I'd be happy to show it to you. If you want to analyze the coefficients and decide which conic the equation represents, we could do that too.

 

[ahmadriaz]

sir...my current program can analyse the type of conic...i just need help in how to draw graph of eqs of the form
10x^2+4y^2+3xy+4x+6y+8=0

my current program finds the vertices, directrices, axxis, centre, etc...

 

[chaoseverlasting]

If you could show us the code, perhaps we could look at it and tell you. If you've got everything else sorted out and are using Borland Turbo C++ 3.0 or thereabouts, the compiler has a graphics library, graphics.h. Look into the examples for the function initgraph(). You basically need initgraph(), putpixel(), and closegraph() for actual plotting.

You will be restricted to 16 colors, and you would get the best resolution using parametric equations. To further streamline the code, you would need to use symmetry to plot the points. To do that, I would suggest that after you figure out what conic it is that you want to plot, you try to reduce it to its general equation and plot that instead of the general second degree equation. You would need to solve some of this on paper before you could program it in, but that shouldn't be too difficult.

 

[ahmadriaz]

well i am using flash mx...n i have done the DIFICULT PAPER WORK..i have reduced the conics to their general forms...but i think those general forms are the ROTATED equations...if u plot them/...i will only get a standard curse with axis x=0 or y=0...but the actual curve is rotated at some angle right?i am having problem with that...and how to show you the code of FLASH..i will have to send u abc.FLA file for that,,,,but isn't there any method for ploting GENERAL EQ of CONICS>>>?without using those graphics libraries?i mean how to find out the cordinates?i can plot them in flash..but i dun know how to find coordinated...can POLAR FORM be suitable for this>??

 

[chaoseverlasting]

Yeah, youre right. In most cases you will get a rotated axis. You can counter for that of course by assuming that the original axis differs from the rotated axis by an angle $$\theta$$ and the rotated coordinates are:

$$x*=xcos\theta - ysin\theta$$
$$y*=xsin\theta + ycos\theta$$ where x and y are the original coordinates and x*, y* are the coordinates you see in your equation.

I don't know much about flash, all the code I've written is in C++, I was thinking along the lines of reducing the general equation to the standard form and from there to the parametric form to get better resolution. Like I said before, you can get very good resolution with polar form.