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with(geometry); Apollonius, AreCollinear, AreConcurrent, AreConcyclic, AreConjugate, AreHarmonic, AreOrthogonal, AreParallel, ArePerpendicular, AreSimilar, AreTangent, CircleOfSimilitude, CrossProduct, CrossRatio, DefinedAs, Equation, EulerCircle, EulerLine, ExteriorAngle, ExternalBisector, FindAngle, GergonnePoint, GlideReflection, HorizontalCoord, HorizontalName, InteriorAngle, IsEquilateral, IsOnCircle, IsOnLine, IsRightTriangle, MajorAxis, MakeSquare, MinorAxis, NagelPoint, OnSegment, ParallelLine, PedalTriangle, PerpenBisector, PerpendicularLine, Polar, Pole, RadicalAxis, RadicalCenter, RegularPolygon, RegularStarPolygon, SensedMagnitude, SimsonLine, SpiralRotation, StretchReflection, StretchRotation, TangentLine, VerticalCoord, VerticalName, altitude, apothem, area, asymptotes, bisector, center, centroid, circle, circumcircle, conic, convexhull, coordinates, detail, diagonal, diameter, dilatation, directrix, distance, draw, dsegment, ellipse, excircle, expansion, foci, focus, form, homology, homothety, hyperbola, incircle, inradius, intersection, inversion, line, medial, median, method, midpoint, orthocenter, parabola, perimeter, point, powerpc, projection, radius, randpoint, reciprocation, reflection, rotation, segment, sides, similitude, slope, square, stretch, tangentpc, translation, triangle, vertex, vertices with(plots); animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot with(plots,implicitplot); implicitplot *Excercici1. ex1:=((x+2)^2)/((sqrt(15)^3)+(y^2)/((sqrt((15)/(8)))^2))=1; ex1 d x C 2 2 15 15 C 8 y 2 15
d:=expand((x+2)^2); d d x 2 C 4 x C 4
dd:=(d+8*y^2)= dd d x 2 C 8 y 2 C 4 x C 4 = 15 Excercici ados:=x^2+4y=0; ados d x 2 C 4 y = 0 conic(c1,ados,[x,y]); c form(c1); parabola2d detail(c1);
name of the object c form of the object ellipse2d center K2, 0 foci K 2 K 2 5 , 0 , K 2 C 2 5 , 0 length of the major axis 4 6 length of the minor axis 4 equation of the ellipse x 2 C 6 y 2 C 4 x K 20 = 0 implicitplot(bdos,scaling=constrained); x
K 6 K 5 K 4 K 3 K 2 K 1 0 1 2
y K 2
K 1
cdos:=2(x+1)^2+4(y-1)^2=16; cdos d 2 x C 1 2 C 4 y K 1 2 = 16 conic(c3,cdos,[x,y]); c detail(c3);
name of the object c form of the object ellipse2d center K1, 1 foci K3, 1 , 1, 1 length of the major axis 4 2 length of the minor axis 4 equation of the ellipse 2 x 2 C 4 y 2 C 4 x K 8 y K 10 = 0 implicitplot(cdos,scaling=constrained); x
K 3 K 2 K 1 0 1
y K 1
Excercici restart; with(geometry):with(plots):with(plots,implicitplot): eq:=4x-x^2+4*y-12=0;
K0.7 K0.6 K0.5 K0.4 K0.
f2:=pointplot([1/2, 1]);
b:=implicitplot([e,d],color=[red,blue],scaling=constrained)
x
K 1 K0.5 0 0.5 1
y
Excercici 4 restart; with(geometry):with(plots):with(plots,implicitplot): eq:=x^2-2x+1+9*y^2= eq d x 2 C 9 y 2 K 2 x C 1 = 9 conic(c1,eq,[x,y]); c
detail(c 1 ) name of the object c form of the object ellipse2d center 1, 0 foci 1 K 2 2 , 0 , 1 C 2 2 , 0 length of the major axis 6 length of the minor axis 2 equation of the ellipse x 2 C 9 y 2 K 2 x K 8 = 0 form(c1) ellipse2d *Excercici
restart; with(geometry):with(plots):with(plots,implicitplot): eq:=x^2-y^2= eq d x 2 K y 2 = 1 conic(c1,eq,[x,y]); c detail(c1) name of the object c form of the object hyperbola2d center 0, 0 foci K 2 , 0 , 2 , 0 vertices K1, 0 , 1, 0 the asymptotes y C x = 0, y K x = 0 equation of the hyperbola x 2 K y 2 K 1 = 0 form(c1) hyperbola2d
*Exercici 7 restart; with(geometry):with(plots):with(plots,implicitplot): eq:=-x^2-x+2=y eq d Kx 2 K x C 2 = y conic(c1,eq,[x,y]); c form(c1); parabola2d detail(c1); name of the object c form of the object parabola2d vertex K
focus K
directrix y K
equation of the parabola Kx 2 K x K y C 2 = 0 implicitplot(eq);
eq:=x^2-2*x+1+y^2= eq d x 2 C y 2 K 2 x C 1 = 9 conic(c1,eq,[x,y]); ellipse: the given equation is indeed a circle c form(c1) circle2d detail(c1) name of the object c form of the object circle2d name of the center center_c coordinates of the center 1, 0 radius of the circle 9 equation of the circle x 2 C y 2 K 2 x K 8 = 0 implicitplot(eq); x
K 2 K 1 0 1 2 3 4
y K 3
K 2
K 1
*Excercici 9
restart; with(geometry):with(plots):with(plots,implicitplot): eq:=(x-4)^2-((y+5)^2)/(3)=1; eq d x K 4 2 K y C 5 2 3
conic(c1,eq,[x,y]); c h:=implicitplot(eq);
x
K 4 K 2 0 2 4 6 8
y K 30
K 20
K 10
b:=implicitplot(x-4=-(y+5)/(3))
x
K 1 0 1 2 3 4
y K 5
display(a,b,h)
