Re: new user help

*To*: mathgroup at smc.vnet.net*Subject*: [mg13368] Re: [mg13296] new user help*From*: BobHanlon at aol.com*Date*: Mon, 20 Jul 1998 02:50:21 -0400*Sender*: owner-wri-mathgroup at wolfram.com

John, eqn = -4*a*x + 6*a*y - 4*a == a*x^2 + a*y^2; Since the equation is not of the form lhs == 0 and the coefficients of x^2 and y^2 are not unity, it will be manipulated into the preferred form first. eqn[[1]] -4*a - 4*a*x + 6*a*y eqn[[2]] a*x^2 + a*y^2 temp = eqn[[1]]-eqn[[2]]; temp == 0 -4*a - 4*a*x - a*x^2 + 6*a*y - a*y^2 == 0 Coefficient[temp, x^2] -a temp = (temp/% // Simplify); temp == 0 4 + 4*x + x^2 - 6*y + y^2 == 0 h = -Coefficient[temp, x]/2 -2 k = -Coefficient[temp, y]/2 3 stdEqn = (x - h)^2 + (y - k)^2 == r^2 // ExpandAll 13 + 4*x + x^2 - 6*y + y^2 == r^2 temp == 0 4 + 4*x + x^2 - 6*y + y^2 == 0 Comparing term-by-term, then r^2 = 9; or Solve[{temp == 0, stdEqn}, r, {x, y}] {{r -> -3}, {r -> 3}} (x - h)^2 + (y - k)^2 == r^2 /. %[[1]] (2 + x)^2 + (-3 + y)^2 == 9 % // ExpandAll // Simplify 4 + 4*x + x^2 - 6*y + y^2 == 0 Combining all of these steps into a function: stdEllipse[eqn_, x_Symbol:x, y_Symbol:y] := Module[{stdEqn, h, k, r, temp}, temp = eqn[[1]] - eqn[[2]]; temp = temp/Coefficient[temp, x^2]; h = -Coefficient[temp, x]/2; k = -Coefficient[temp, y]/2; stdEqn = (x - h)^2 + (y - k)^2 == r^2; stdEqn /. Solve[{temp == 0, stdEqn}, r, {x, y}][[1]]]; stdEllipse[a x^2+a y^2==-4a x+6a y-4a] (2 + x)^2 + (-3 + y)^2 == 9 stdEllipse[z^2+t^2+10z-8t+16==0, z, t] (-4 + t)^2 + (5 + z)^2 == 25 stdEllipse[x^2+y^2-x-y+2==0] (-(1/2) + x)^2 + (-(1/2) + y)^2 == -(3/2) Clear[a, b, c]; stdEllipse[x^2 + y^2 + a*x + b*y + c == 0] (a/2 + x)^2 + (b/2 + y)^2 == 1/4*(a^2 + b^2 - 4*c) Bob Hanlon In a message dated 7/17/98 10:43:09 AM, john at dlugosz.com wrote: >I'm lost. I just don't know how to get started... > >The excersize I've chosen for myself is to start with > > x^2+y^2+4x-6y+4==0 > >and manipulate it into the form (x-h)^2+(y-k)^2==r^2 > >So... how do I "manipulate" the equasion? The functions like Expand, >Factor, etc. don't help much. I my calculator (an HP48) I can point to >specific subexpressions and apply operations to them, like factor, >distribute, changing forms, etc. > >How do I collect the x's together in parens, the y's in parens, and >complete the squares? Doing it on paper defeats the point! I want to >learn how to "do math" using this tool. That's more than just asking >"OK, what's X?". It means manipulating things and arranging them, >getting to know how the symbols all fit together.