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Problemas populares de Geometry

vértices (x^2}{25}+\frac{y^2)/9 =1	vertices\:\frac{x^{2}}{25}+\frac{y^{2}}{9}=1
x^2-(y^2)/(16)=1	x^{2}-\frac{y^{2}}{16}=1
vértices f(x)=(x-5)(x+1)	vertices\:f(x)=(x-5)(x+1)
x^2+(y-4)^2=4	x^{2}+(y-4)^{2}=4
eje x^2-6x+5y=-34	axis\:x^{2}-6x+5y=-34
vértices f(x)=x^2-2x-3	vertices\:f(x)=x^{2}-2x-3
y+x^2=4x	y+x^{2}=4x
asíntotas (x^2}{36}-\frac{y^2)/9 =1	asymptotes\:\frac{x^{2}}{36}-\frac{y^{2}}{9}=1
directriz x^2=8y	directrix\:x^{2}=8y
focos y^2=32x	foci\:y^{2}=32x
focos 16x^2-9y^2=144	foci\:16x^{2}-9y^{2}=144
vértices 3x^2+y^2+18x-2y-8=0	vertices\:3x^{2}+y^{2}+18x-2y-8=0
directriz x^2=12y	directrix\:x^{2}=12y
x^2+y^2-6x+4y+4=0	x^{2}+y^{2}-6x+4y+4=0
directriz y= 1/2 x^2	directrix\:y=\frac{1}{2}x^{2}
focos (y^2)/9-(x^2)/4 =1	foci\:\frac{y^{2}}{9}-\frac{x^{2}}{4}=1
x^2=3y	x^{2}=3y
(a+1)/b =(a-1)/b+(b+1)/a	\frac{a+1}{b}=\frac{a-1}{b}+\frac{b+1}{a}
focos (x^2)/4+(y^2)/9 =1	foci\:\frac{x^{2}}{4}+\frac{y^{2}}{9}=1
directriz y^2-y-x+1=0	directrix\:y^{2}-y-x+1=0
((x-5)^2)/4+((y+3)^2)/(16)=1	\frac{(x-5)^{2}}{4}+\frac{(y+3)^{2}}{16}=1
x^2=6y	x^{2}=6y
focos ((y-3)^2}{11}-\frac{(x+1)^2)/5 =1	foci\:\frac{(y-3)^{2}}{11}-\frac{(x+1)^{2}}{5}=1
x^2+2x+y^2+4y=20	x^{2}+2x+y^{2}+4y=20
x-y^2=0	x-y^{2}=0
x^2+y^2-4x=0	x^{2}+y^{2}-4x=0
x^2+y^2-2x-4y+1=0	x^{2}+y^{2}-2x-4y+1=0
4x^2-y^2-24x-4y+28=0	4x^{2}-y^{2}-24x-4y+28=0
solvefor y,x^2=y^2	solvefor\:y,x^{2}=y^{2}
x^2+y^2+10x-4y-7=0	x^{2}+y^{2}+10x-4y-7=0
focos y^2=-10x	foci\:y^{2}=-10x
x^2=8y	x^{2}=8y
focos (x+6)^2+((y+4)^2)/(1/4)=1	foci\:(x+6)^{2}+\frac{(y+4)^{2}}{\frac{1}{4}}=1
(x^2)/(25)+(y^2)/(16)=1	\frac{x^{2}}{25}+\frac{y^{2}}{16}=1
vértices (y^2)/(36)-(x^2)/(64)=1	vertices\:\frac{y^{2}}{36}-\frac{x^{2}}{64}=1
x^2+(y+2)^2=4	x^{2}+(y+2)^{2}=4
x=4y^2+8y-3	x=4y^{2}+8y-3
(x^2)/(16)+y^2=1	\frac{x^{2}}{16}+y^{2}=1
y^2=-20x	y^{2}=-20x
x^2-4x-8y+2=0	x^{2}-4x-8y+2=0
3x^2-15y^2+2x-3y=4	3x^{2}-15y^{2}+2x-3y=4
x^2+y^2=3	x^{2}+y^{2}=3
vértices (x-12)^2-156	vertices\:(x-12)^{2}-156
focos y^2=-4x	foci\:y^{2}=-4x
directriz y^2=4x	directrix\:y^{2}=4x
directriz (y-7)^2=-12(x+1)	directrix\:(y-7)^{2}=-12(x+1)
focos x^2=-16y	foci\:x^{2}=-16y
focos x^2	foci\:x^{2}
focos ((x-3)^2)/5+((y-1)^2)/(15)=1	foci\:\frac{(x-3)^{2}}{5}+\frac{(y-1)^{2}}{15}=1
focos (x^2)/(100)+(y^2)/(64)=1	foci\:\frac{x^{2}}{100}+\frac{y^{2}}{64}=1
focos (x^2)/4+(y^2)/(16)=1	foci\:\frac{x^{2}}{4}+\frac{y^{2}}{16}=1
focos 3x^2+2y^2=6	foci\:3x^{2}+2y^{2}=6
vértices (x^2}{25}+\frac{y^2)/4 =1	vertices\:\frac{x^{2}}{25}+\frac{y^{2}}{4}=1
4x^2+y^2=16	4x^{2}+y^{2}=16
focos y^2=-8x	foci\:y^{2}=-8x
x=y^2-5	x=y^{2}-5
vértices y=x^2+2x-3	vertices\:y=x^{2}+2x-3
(x^2)/(25)+(y^2)/(36)=1	\frac{x^{2}}{25}+\frac{y^{2}}{36}=1
vértices 2x^2	vertices\:2x^{2}
focos 4y^2-25x^2=100	foci\:4y^{2}-25x^{2}=100
-9x^2+y^2-72x-153=0	-9x^{2}+y^{2}-72x-153=0
vértices f(x)=x^2-2x-15	vertices\:f(x)=x^{2}-2x-15
x^2-9y^2=9	x^{2}-9y^{2}=9
focos (x^2)/(36)+(y^2)/(100)=1	foci\:\frac{x^{2}}{36}+\frac{y^{2}}{100}=1
vértices f(x)=-x^2-2x+3	vertices\:f(x)=-x^{2}-2x+3
x^2+y^2=4	x^{2}+y^{2}=4
9y^2-16x^2-256=0	9y^{2}-16x^{2}-256=0
(x^2)/(25)-(y^2)/(36)=1	\frac{x^{2}}{25}-\frac{y^{2}}{36}=1
-x^2-6x+y-8=0	-x^{2}-6x+y-8=0
x^2+y^2-2x+4y-4=0	x^{2}+y^{2}-2x+4y-4=0
directriz x=-1/12 y^2	directrix\:x=-\frac{1}{12}y^{2}
4x^2+9y^2-16x+18y=11	4x^{2}+9y^{2}-16x+18y=11
(x^2)/4+(y^2)/1 =1	\frac{x^{2}}{4}+\frac{y^{2}}{1}=1
vértices x^2	vertices\:x^{2}
focos y^2=-12x	foci\:y^{2}=-12x
9x^2-y^2-36x-6y+18=0	9x^{2}-y^{2}-36x-6y+18=0
9y^2-16x^2=144	9y^{2}-16x^{2}=144
(x-1)^2+y^2=1	(x-1)^{2}+y^{2}=1
focos 16x^2+25y^2=400	foci\:16x^{2}+25y^{2}=400
vértices (x^2)/(25)+(y^2)/(16)=1	vertices\:\frac{x^{2}}{25}+\frac{y^{2}}{16}=1
4<=-x^2-y	4\le\:-x^{2}-y
18x^2-64x-14y+150=0	18x^{2}-64x-14y+150=0
x^2+y^2+6x-4y-12=0	x^{2}+y^{2}+6x-4y-12=0
excentricidad 36x^2+y^2=36	eccentricity\:36x^{2}+y^{2}=36
x^2-4x+y^2+6y-12=0	x^{2}-4x+y^{2}+6y-12=0
(x^2}{16}+\frac{y^2)/4 =1	\frac{x^{2}}{16}+\frac{y^{2}}{4}=1
directriz x^2=-4y	directrix\:x^{2}=-4y
y^2=4-x^2	y^{2}=4-x^{2}
asíntotas (x^2)/4-(y^2)/4 =1	asymptotes\:\frac{x^{2}}{4}-\frac{y^{2}}{4}=1
eje (x^2)/9-(y^2)/4 =1	axis\:\frac{x^{2}}{9}-\frac{y^{2}}{4}=1
focos (y^2)/(36)-(x^2)/(64)=1	foci\:\frac{y^{2}}{36}-\frac{x^{2}}{64}=1
x=y-y^2	x=y-y^{2}
y^2-8x=0	y^{2}-8x=0
x^2-2x+y^2+2y=7	x^{2}-2x+y^{2}+2y=7
focos (y^2)/(49)-(x^2)/(64)=1	foci\:\frac{y^{2}}{49}-\frac{x^{2}}{64}=1
solvefor y,36x^2-25y^2+144x-50y+119=0	solvefor\:y,36x^{2}-25y^{2}+144x-50y+119=0
asíntotas (x^2)/(100)-(y^2)/(64)=1	asymptotes\:\frac{x^{2}}{100}-\frac{y^{2}}{64}=1
x^2+y^2<= 4	x^{2}+y^{2}\le\:4
vértices f(x)=x^2+4x+3	vertices\:f(x)=x^{2}+4x+3
directriz y= 1/12 x^2	directrix\:y=\frac{1}{12}x^{2}

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