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Problemas populares de Geometry

(x^2)/(144)+(y^2)/(169)=1	\frac{x^{2}}{144}+\frac{y^{2}}{169}=1
4x^2-25y^2+100y=200	4x^{2}-25y^{2}+100y=200
vértices f(x)=x^2-3	vertices\:f(x)=x^{2}-3
asíntotas 16x^2-9y^2=144	asymptotes\:16x^{2}-9y^{2}=144
y^2=-9x	y^{2}=-9x
x^2+20x+y^2+16y=-20	x^{2}+20x+y^{2}+16y=-20
asíntotas (x^2)/(64)-(y^2)/(36)=1	asymptotes\:\frac{x^{2}}{64}-\frac{y^{2}}{36}=1
x^2+y^2-6x+2y+9=0	x^{2}+y^{2}-6x+2y+9=0
focos 4x^2+y^2=16	foci\:4x^{2}+y^{2}=16
vértices y=x^2-24x-12	vertices\:y=x^{2}-24x-12
x=4y^2	x=4y^{2}
(x^2)/(36)+(y^2)/(49)=1	\frac{x^{2}}{36}+\frac{y^{2}}{49}=1
y^2=-6x	y^{2}=-6x
y^2-4x+4y-4=0	y^{2}-4x+4y-4=0
focos (x^2)/(49)-(y^2)/(16)=1	foci\:\frac{x^{2}}{49}-\frac{y^{2}}{16}=1
16x^2+25y^2=400	16x^{2}+25y^{2}=400
focos (x^2}{25}+\frac{y^2)/9 =1	foci\:\frac{x^{2}}{25}+\frac{y^{2}}{9}=1
vértices 9x^2-4y^2=36	vertices\:9x^{2}-4y^{2}=36
focos (x^2)/4-(y^2)/(16)=1	foci\:\frac{x^{2}}{4}-\frac{y^{2}}{16}=1
x^2-y^2=3	x^{2}-y^{2}=3
9x^2+4y^2-18x+16y-11=0	9x^{2}+4y^{2}-18x+16y-11=0
x^2+16y^2=16	x^{2}+16y^{2}=16
vértices f(x)=x^2-2x+1	vertices\:f(x)=x^{2}-2x+1
y^2=-10x	y^{2}=-10x
vértices f(x)=x^2-6x+5	vertices\:f(x)=x^{2}-6x+5
(x^2}{16}+\frac{y^2)/7 =1	\frac{x^{2}}{16}+\frac{y^{2}}{7}=1
x^2+y=1	x^{2}+y=1
x=y^2-3	x=y^{2}-3
x^2-y^2=49	x^{2}-y^{2}=49
focos (y^2)/(49)-(x^2)/(25)=1	foci\:\frac{y^{2}}{49}-\frac{x^{2}}{25}=1
9x^2-4y^2-72x=0	9x^{2}-4y^{2}-72x=0
x^2+y^2+6x+2y+6=0	x^{2}+y^{2}+6x+2y+6=0
(x^2)/(100)+(y^2)/(36)=1	\frac{x^{2}}{100}+\frac{y^{2}}{36}=1
4x^2-y^2=16	4x^{2}-y^{2}=16
x^2+2y^2-2x+8y+5=0	x^{2}+2y^{2}-2x+8y+5=0
(x-1)^2+(y-1)^2=2	(x-1)^{2}+(y-1)^{2}=2
x^2+y^2=5	x^{2}+y^{2}=5
(x^2}{36}-\frac{y^2)/4 =1	\frac{x^{2}}{36}-\frac{y^{2}}{4}=1
eje 5x^2+30x+24y=51	axis\:5x^{2}+30x+24y=51
y^2-12y-4x+28=0	y^{2}-12y-4x+28=0
directriz y^2=20x	directrix\:y^{2}=20x
x^2+y^2+4x-18y+81=0	x^{2}+y^{2}+4x-18y+81=0
vértices x^2=20y	vertices\:x^{2}=20y
y^2=16x	y^{2}=16x
y^2=-24x	y^{2}=-24x
9x^2-16y^2+36x+32y-124=0	9x^{2}-16y^{2}+36x+32y-124=0
4x^2+4y^2+36y+5=0	4x^{2}+4y^{2}+36y+5=0
focos x^2+(y^2)/(64)=1	foci\:x^{2}+\frac{y^{2}}{64}=1
(x^2)/9+(y^2)/9 =1	\frac{x^{2}}{9}+\frac{y^{2}}{9}=1
x=y^2-1	x=y^{2}-1
((x-3)^2)/(81)-((y+5)^2)/(144)=1	\frac{(x-3)^{2}}{81}-\frac{(y+5)^{2}}{144}=1
focos x= 1/4 y^2	foci\:x=\frac{1}{4}y^{2}
x^2+y^2-4y=0	x^{2}+y^{2}-4y=0
focos x^2=-8y	foci\:x^{2}=-8y
vértices f(x)=(x-3)^2	vertices\:f(x)=(x-3)^{2}
x^2+9y^2+6x-90y+225=0	x^{2}+9y^{2}+6x-90y+225=0
focos x^2=-4y	foci\:x^{2}=-4y
x^2+y^2+10x+12y+25=0	x^{2}+y^{2}+10x+12y+25=0
vértices x^2=16y	vertices\:x^{2}=16y
directriz y^2=-10x	directrix\:y^{2}=-10x
excentricidad (x^2)/(25)+(y^2)/(25)=1	eccentricity\:\frac{x^{2}}{25}+\frac{y^{2}}{25}=1
vértices f(x)=x^2-4	vertices\:f(x)=x^{2}-4
-x^2+9y^2+4x+54y+68=0	-x^{2}+9y^{2}+4x+54y+68=0
directriz x=-1/8 y^2	directrix\:x=-\frac{1}{8}y^{2}
asíntotas 4x^2-y^2=16	asymptotes\:4x^{2}-y^{2}=16
x^2+y^2-4x-4y=0	x^{2}+y^{2}-4x-4y=0
x^2=-4y	x^{2}=-4y
excentricidad (x^2}{25}+\frac{y^2)/9 =1	eccentricity\:\frac{x^{2}}{25}+\frac{y^{2}}{9}=1
x=y^2-4	x=y^{2}-4
focos ((x-5)^2)/4+((y+3)^2)/(16)=1	foci\:\frac{(x-5)^{2}}{4}+\frac{(y+3)^{2}}{16}=1
(x-2)^2=8y	(x-2)^{2}=8y
vértices y=2-x-2x^2	vertices\:y=2-x-2x^{2}
(x^2}{36}+\frac{y^2)/9 =1	\frac{x^{2}}{36}+\frac{y^{2}}{9}=1
centro x^2+y^2-14x+2y+41=0	center\:x^{2}+y^{2}-14x+2y+41=0
vértices y=x^2+3	vertices\:y=x^{2}+3
focos ((x+2)^2)/9+((y-3)^2)/(16)=1	foci\:\frac{(x+2)^{2}}{9}+\frac{(y-3)^{2}}{16}=1
(x^2)/(64)+(y^2)/(16)=1	\frac{x^{2}}{64}+\frac{y^{2}}{16}=1
asíntotas (x^2)/(36)-(y^2)/(64)=1	asymptotes\:\frac{x^{2}}{36}-\frac{y^{2}}{64}=1
x^2+y^2-25=0	x^{2}+y^{2}-25=0
vértices (x^2)/7+(y^2)/(16)=1	vertices\:\frac{x^{2}}{7}+\frac{y^{2}}{16}=1
focos (x^2)/(16)+(y^2)/(25)=1	foci\:\frac{x^{2}}{16}+\frac{y^{2}}{25}=1
focos x^2-y^2=14	foci\:x^{2}-y^{2}=14
(x^2)/4+(y^2)/(16)=1	\frac{x^{2}}{4}+\frac{y^{2}}{16}=1
16x^2+192x+576+25y^2=1600	16x^{2}+192x+576+25y^{2}=1600
x^2+y^2-10x-10y+25=0	x^{2}+y^{2}-10x-10y+25=0
x^2-y^2=1	x^{2}-y^{2}=1
centro x^2+y^2-32x-60y+1122=0	center\:x^{2}+y^{2}-32x-60y+1122=0
directriz x^2	directrix\:x^{2}
focos (x^2}{36}+\frac{y^2)/9 =1	foci\:\frac{x^{2}}{36}+\frac{y^{2}}{9}=1
directriz x^2-4y=0	directrix\:x^{2}-4y=0
focos ((x-4)^2}{36}-\frac{(y-2)^2)/9 =1	foci\:\frac{(x-4)^{2}}{36}-\frac{(y-2)^{2}}{9}=1
vértices x^2=4y-2y^2	vertices\:x^{2}=4y-2y^{2}
x=(y-5)^2	x=(y-5)^{2}
(x-2)^2=12(y+3)	(x-2)^{2}=12(y+3)
(y-2)^2=12(x+1)	(y-2)^{2}=12(x+1)
vértices f(x)=x^2+2x	vertices\:f(x)=x^{2}+2x
vértices (x^2)/(64)+(y^2)/(16)=1	vertices\:\frac{x^{2}}{64}+\frac{y^{2}}{16}=1
focos 2x^2+y^2=2	foci\:2x^{2}+y^{2}=2
y^2+6y+9=x+8	y^{2}+6y+9=x+8
focos x^2+4x-4y=0	foci\:x^{2}+4x-4y=0

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