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Problemas populares de Geometry

vértices (x^2)/9+(y^2)/(25)=1	vertices\:\frac{x^{2}}{9}+\frac{y^{2}}{25}=1
9(x-1)^2-16(y+2)^2=144	9(x-1)^{2}-16(y+2)^{2}=144
vértices 9x^2+4y^2+36x-24y+36=0	vertices\:9x^{2}+4y^{2}+36x-24y+36=0
vértices f(x)=3x^2-18x+23	vertices\:f(x)=3x^{2}-18x+23
x^2+y^2<= 25	x^{2}+y^{2}\le\:25
2x^2+y^2=2	2x^{2}+y^{2}=2
(x-3)^2+y^2=4	(x-3)^{2}+y^{2}=4
directriz y=-4x^2	directrix\:y=-4x^{2}
vértices (x^2}{25}-\frac{y^2)/9 =1	vertices\:\frac{x^{2}}{25}-\frac{y^{2}}{9}=1
x^2-2x-4y+9=0	x^{2}-2x-4y+9=0
4x^2+25y^2=100	4x^{2}+25y^{2}=100
directriz x^2=4y	directrix\:x^{2}=4y
x^2=-16y	x^{2}=-16y
y-x>-x^2-1	y-x>-x^{2}-1
((y+1)^2)/4-(x-5)^2=4	\frac{(y+1)^{2}}{4}-(x-5)^{2}=4
focos x= 1/8 y^2	foci\:x=\frac{1}{8}y^{2}
x^2-4y^2-2x+16y=20	x^{2}-4y^{2}-2x+16y=20
asíntotas 9x^2-4y^2-72x=0	asymptotes\:9x^{2}-4y^{2}-72x=0
focos y=2x^2	foci\:y=2x^{2}
(x^2)/7+(y^2)/(16)=1	\frac{x^{2}}{7}+\frac{y^{2}}{16}=1
x^2=y+2	x^{2}=y+2
directriz x^2=24y	directrix\:x^{2}=24y
2x^2+16y=0	2x^{2}+16y=0
radio x^2+y^2=25	radius\:x^{2}+y^{2}=25
9x^2-54x+25y^2-200y=-256	9x^{2}-54x+25y^{2}-200y=-256
y^2=2x	y^{2}=2x
vérticeparabola y=x^2-24x-12	vertexparabola\:y=x^{2}-24x-12
focos (x^2}{16}-\frac{y^2)/9 =1	foci\:\frac{x^{2}}{16}-\frac{y^{2}}{9}=1
x^2-12x+16y+68=0	x^{2}-12x+16y+68=0
10x^2+4y^2+2x+16y=144	10x^{2}+4y^{2}+2x+16y=144
y^2=-36x	y^{2}=-36x
x^2=4y	x^{2}=4y
vértices f(x)=x^2-9	vertices\:f(x)=x^{2}-9
y^2=x-3	y^{2}=x-3
((x-5)^2}{25}+\frac{(y+3)^2)/9 =1	\frac{(x-5)^{2}}{25}+\frac{(y+3)^{2}}{9}=1
focos 16y^2-25x^2=400	foci\:16y^{2}-25x^{2}=400
excentricidad 16x^2+25y^2=400	eccentricity\:16x^{2}+25y^{2}=400
x^2+y^2=25	x^{2}+y^{2}=25
(x^2)/(64)+(y^2)/(36)=1	\frac{x^{2}}{64}+\frac{y^{2}}{36}=1
x^2+y^2=6	x^{2}+y^{2}=6
x^2=16y	x^{2}=16y
(x^2}{16}+\frac{y^2)/9 =1	\frac{x^{2}}{16}+\frac{y^{2}}{9}=1
-9x^2+4y^2-36x-16y-164=0	-9x^{2}+4y^{2}-36x-16y-164=0
directriz 1/4 (y+3)=(x-2)^2	directrix\:\frac{1}{4}(y+3)=(x-2)^{2}
x=-2y^2	x=-2y^{2}
x^2+y^2=36	x^{2}+y^{2}=36
focos (x^2)/7+(y^2)/(16)=1	foci\:\frac{x^{2}}{7}+\frac{y^{2}}{16}=1
y^2= 7/2 x	y^{2}=\frac{7}{2}x
directriz x^2=-8y	directrix\:x^{2}=-8y
directriz y^2=3x	directrix\:y^{2}=3x
(x^2)/4-y^2=1	\frac{x^{2}}{4}-y^{2}=1
focos (x^2}{25}+\frac{y^2)/4 =1	foci\:\frac{x^{2}}{25}+\frac{y^{2}}{4}=1
vértices y=-(x^2)/(10)+(9x)/(10)+11/5	vertices\:y=-\frac{x^{2}}{10}+\frac{9x}{10}+\frac{11}{5}
2y^2-12y-x+5=0	2y^{2}-12y-x+5=0
excentricidad 9x^2+9y^2+18x-18y+14=0	eccentricity\:9x^{2}+9y^{2}+18x-18y+14=0
focos x^2=8y	foci\:x^{2}=8y
y^2+4x=7	y^{2}+4x=7
vértices (x^2}{16}-\frac{y^2)/9 =1	vertices\:\frac{x^{2}}{16}-\frac{y^{2}}{9}=1
focos 9x^2-16y^2=144	foci\:9x^{2}-16y^{2}=144
asíntotas (y^2}{16}-\frac{x^2)/9 =1	asymptotes\:\frac{y^{2}}{16}-\frac{x^{2}}{9}=1
x=2y^2	x=2y^{2}
vértices f(x)=x^2-6x+1	vertices\:f(x)=x^{2}-6x+1
eje x^2+(y^2)/(64)=1	axis\:x^{2}+\frac{y^{2}}{64}=1
x^2-y=0	x^{2}-y=0
y^2=-4x	y^{2}=-4x
vértices 9x^2-4y^2-90x-32y=-305	vertices\:9x^{2}-4y^{2}-90x-32y=-305
vértices f(x)=3x^2-6x+4	vertices\:f(x)=3x^{2}-6x+4
vértices 16x^2-9y^2=144	vertices\:16x^{2}-9y^{2}=144
y^2=8x	y^{2}=8x
focos ((x-2)^2)/(36)+((y+1)^2)/(25)=1	foci\:\frac{(x-2)^{2}}{36}+\frac{(y+1)^{2}}{25}=1
asíntotas (x^2)/9-(y^2)/(16)=1	asymptotes\:\frac{x^{2}}{9}-\frac{y^{2}}{16}=1
(x^2)/9+(y^2)/(25)=1	\frac{x^{2}}{9}+\frac{y^{2}}{25}=1
focos 9x^2-y^2-36x-6y+18=0	foci\:9x^{2}-y^{2}-36x-6y+18=0
focos (x^2)/(25)+(y^2)/(49)=1	foci\:\frac{x^{2}}{25}+\frac{y^{2}}{49}=1
área (x^2)/(a^2)+(y^2)/(b^2)=1	area\:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1
(x^2}{36}+\frac{y^2)/4 =1	\frac{x^{2}}{36}+\frac{y^{2}}{4}=1
vértices f(x)=x^2-10x+24	vertices\:f(x)=x^{2}-10x+24
vértices (x^2}{16}+\frac{y^2)/4 =1	vertices\:\frac{x^{2}}{16}+\frac{y^{2}}{4}=1
vértices f(x)=x^2-8x+12	vertices\:f(x)=x^{2}-8x+12
asíntotas (y^2)/(36)-(x^2)/(64)=1	asymptotes\:\frac{y^{2}}{36}-\frac{x^{2}}{64}=1
vértices ((x-3)^2)/5+((y-1)^2)/(15)=1	vertices\:\frac{(x-3)^{2}}{5}+\frac{(y-1)^{2}}{15}=1
3x^2-y^2=11	3x^{2}-y^{2}=11
9x^2+16y^2=144	9x^{2}+16y^{2}=144
x^2+y^2=10	x^{2}+y^{2}=10
focos x^2+(y^2)/(25)=1	foci\:x^{2}+\frac{y^{2}}{25}=1
(x+2)^2+((y+4)^2)/(1/4)=1	(x+2)^{2}+\frac{(y+4)^{2}}{\frac{1}{4}}=1
(x^2}{16}-\frac{y^2)/9 =1	\frac{x^{2}}{16}-\frac{y^{2}}{9}=1
asíntotas 9y^2-4x^2=36	asymptotes\:9y^{2}-4x^{2}=36
x^2-y^2>= 1	x^{2}-y^{2}\ge\:1
directriz x^2=-28y	directrix\:x^{2}=-28y
vértices f(x)=-x^2+4x-3	vertices\:f(x)=-x^{2}+4x-3
3y+4x=-2x^2-14	3y+4x=-2x^{2}-14
focos x^2=20y	foci\:x^{2}=20y
(x^2)/(169)+(y^2)/(25)=1	\frac{x^{2}}{169}+\frac{y^{2}}{25}=1
asíntotas (y^2)/9-(x^2)/4 =1	asymptotes\:\frac{y^{2}}{9}-\frac{x^{2}}{4}=1
2x^2-6x+2y^2+2y=45	2x^{2}-6x+2y^{2}+2y=45
focos x^2-y^2=6	foci\:x^{2}-y^{2}=6
vértices f(x)=x^2+4x+1	vertices\:f(x)=x^{2}+4x+1
vértices (x^2)/9-(y^2)/(25)=1	vertices\:\frac{x^{2}}{9}-\frac{y^{2}}{25}=1
directriz x-2= 1/8 (y+1)^2	directrix\:x-2=\frac{1}{8}(y+1)^{2}

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