Precision := Exact

PrecisionDigits := 6

Notation := Rational

NotationDigits := 6

Branch := Principal

Exponential := Auto

Logarithm := Auto

Trigonometry := Expand

Trigpower := Auto

Angle := Radian

VariableOrder := [x,y,z]

OutputBase := Decimal

InputBase := Decimal

InputMode := Character

CaseMode := Insensitive

DisplayFormat := Normal

TimesOperator := Dot

Precision:=Exact

PrecisionDigits:=6

Notation:=Rational

NotationDigits:=6

Branch:=Principal

Exponential:=Auto

Logarithm:=Auto

Trigonometry:=Expand

Trigpower:=Auto

Angle:=Radian

VariableOrder:=[x,y,z]

OutputBase:=Decimal

InputBase:=Decimal

InputMode:=Character

CaseMode:=Insensitive

DisplayFormat:=Normal

TimesOperator:=Dot

"********************************************************************"

"********************************************************************"

"PARA CALCULAR LOS ELEMENTOS FUDAMENTALES DE UNA CONICA"

"********************************************************************"

a*x^2+b*y^2+c*x*y+d*x+e*y+f=0

"********************************************************************"

CENTROCONICA(a,b,c,d,e,f):=[(c*e-2*b*d)/(4*a*b-c^2),(c*d-2*a*e)/(4*a*b-c^2)]

MACROCENTROCONICA(a,b,c,d,e,f):=[a*x^2+b*y^2+c*x*y+d*x+e*y+f=0,CENTROCONICA(a~
,b,c,d,e,f)]

"********************************************************************"

"EJEMPLO"

MACROCENTROCONICA(2,-1,3,1,-1,1)

"********************************************************************"

CONICAREFERIDACENTRO(a,b,c,d,e,f):=a*x^2*(4*a*b-c^2)+c*x*y*(4*a*b-c^2)+b*y^2*~
(4*a*b-c^2)+a*(4*b*f-e^2)-b*d^2-c*(c*f-d*e)=0

CONICAREFERIDACENTRO(2,-1,3,1,-1,1)

"********************************************************************"

DIRECCIONESASINTOTICASCONICA(a,b,c,d,e,f):=[-(SQRT(c^2-4*a*b)+c)/(2*b),(SQRT(~
c^2-4*a*b)-c)/(2*b)]

ASINTOTASCONICA(a,b,c,d,e,f):=[y-(c*d-2*a*e)/(4*a*b-c^2)=-(SQRT(c^2-4*a*b)+c)~
/(2*b)*(x-(c*e-2*b*d)/(4*a*b-c^2)),y-(c*d-2*a*e)/(4*a*b-c^2)=(SQRT(c^2-4*a*b)~
-c)/(2*b)*(x-(c*e-2*b*d)/(4*a*b-c^2)),?]

ASINTOTASCONICA(2,-1,3,1,-1,1)

"********************************************************************"

MACROCONICACENTROASINTOTAS(a,b,c,d,e,f):=[MACROCENTROCONICA(a,b,c,d,e,f),ASIN~
TOTASCONICA(a,b,c,d,e,f)]

MACROCONICACENTROASINTOTAS(2,3,0,1,-1,-4)

MACROCONICACENTROASINTOTAS(2,-1,3,1,-1,1)

"********************************************************************"

;Sub(User)
BISECTRICESRECTAS(r,s,t,m,n,p):=[x*(r*SQRT(m^2+n^2)-m*SQRT(r^2+s^2))+y*(s*SQR~
T(m^2+n^2)-n*SQRT(r^2+s^2))-p*SQRT(r^2+s^2)+t*SQRT(m^2+n^2)=0,x*(m*SQRT(r^2+s~
^2)+r*SQRT(m^2+n^2))+y*(n*SQRT(r^2+s^2)+s*SQRT(m^2+n^2))+p*SQRT(r^2+s^2)+t*SQ~
RT(m^2+n^2)=0,?]

BISECTRICESRECTAS(2,1,-1,1,-1,3)

"********************************************************************"

COEFICIENTESASINTOTASCONICA(a,b,c,d,e,f):=[-(c^2-4*a*b)^(3/2)+c*(4*a*b-c^2),2~
*b*(4*a*b-c^2),SQRT(c^2-4*a*b)*(2*b*d-c*e)+e*(4*a*b-c^2),-(c^2-4*a*b)^(3/2)+c~
*(c^2-4*a*b),2*b*(c^2-4*a*b),SQRT(c^2-4*a*b)*(2*b*d-c*e)-e*(4*a*b-c^2)]

"********************************************************************"

EJESCONICA(a,b,c,d,e,f):=BISECTRICESRECTAS((COEFICIENTESASINTOTASCONICA(a,b,c~
,d,e,f)) SUB 1,(COEFICIENTESASINTOTASCONICA(a,b,c,d,e,f)) SUB 2,(COEFICIENTES~
ASINTOTASCONICA(a,b,c,d,e,f)) SUB 3,(COEFICIENTESASINTOTASCONICA(a,b,c,d,e,f)~
) SUB 4,(COEFICIENTESASINTOTASCONICA(a,b,c,d,e,f)) SUB 5,(COEFICIENTESASINTOT~
ASCONICA(a,b,c,d,e,f)) SUB 6)

EJESCONICA(2,-1,3,1,-1,1)

"********************************************************************"

MACROCONICA(a,b,c,d,e,f):=[MACROCENTROCONICA(a,b,c,d,e,f),ASINTOTASCONICA(a,b~
,c,d,e,f),EJESCONICA(a,b,c,d,e,f)]

MACROCONICA(2,-1,3,1,-1,1)

MACROCONICA(3,2,-1,0,0,6)

MACROCONICA(3,2,-1,0,0,-6)

MACROCONICA(1,-2,0,0,0,-5)

MACROCONICA(3,2,-1,2,4,-10)

"********************************************************************"

"Estar¡a bien determinar una conica que pase por 5 puntos dados"

"pero parece que le lleva mucho tiempo a DERIVE"

"********************************************************************"

"********************************************************************"