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Problemas populares de Geometry

((x-5)^2)/9+((y-2)^2)/(36)=1	\frac{(x-5)^{2}}{9}+\frac{(y-2)^{2}}{36}=1
100x^2+64y^2-100x-1575=0	100x^{2}+64y^{2}-100x-1575=0
x^2+(y^2)/(29)=1	x^{2}+\frac{y^{2}}{29}=1
100(x^2-x)+16(y^2-4y)=147	100(x^{2}-x)+16(y^{2}-4y)=147
14x^2+9y^2=126	14x^{2}+9y^{2}=126
3x^2+2y^2-18=0	3x^{2}+2y^{2}-18=0
3x^2+4y^2= 1/2	3x^{2}+4y^{2}=\frac{1}{2}
5x^2+9y^2-10x+4=0	5x^{2}+9y^{2}-10x+4=0
3x^{(2)}+y^{(2)}-24x+39=0	3x^{(2)}+y^{(2)}-24x+39=0
(x-1)^2+((y-3)^2)/2 =1	(x-1)^{2}+\frac{(y-3)^{2}}{2}=1
(x-2)^2+(y+1)^2=5-5y^2	(x-2)^{2}+(y+1)^{2}=5-5y^{2}
9(x-1)^2+(4y)^2=36	9(x-1)^{2}+(4y)^{2}=36
(17x^2+9y^2-30y+9)/(16)=0	\frac{17x^{2}+9y^{2}-30y+9}{16}=0
9= 1/(x^2+y^2-7)	9=\frac{1}{x^{2}+y^{2}-7}
x^2+8y^2-12x-16y-36=0	x^{2}+8y^{2}-12x-16y-36=0
((x-3)^2)/8+((y+1)^2)/5 =1	\frac{(x-3)^{2}}{8}+\frac{(y+1)^{2}}{5}=1
((x^{(2)}))/((36))+((y^{(2)}))/((16))=1	\frac{(x^{(2)})}{(36)}+\frac{(y^{(2)})}{(16)}=1
16x^2+36y^2-256x+576y+2752=0	16x^{2}+36y^{2}-256x+576y+2752=0
16x^2+4y^2+32x+32y+16=0	16x^{2}+4y^{2}+32x+32y+16=0
x^2+5y^2=150	x^{2}+5y^{2}=150
36x^2+16y^2=49	36x^{2}+16y^{2}=49
81X^2+49Y^2=3969	81X^{2}+49Y^{2}=3969
9x^2+36y^2-64x-18y-71=36	9x^{2}+36y^{2}-64x-18y-71=36
10x^2+y+2x+y^2=0	10x^{2}+y+2x+y^{2}=0
(x^2)/2+(y^2)/8 =1	\frac{x^{2}}{2}+\frac{y^{2}}{8}=1
(x^2}{49}+\frac{(y-5)^2)/4 =1	\frac{x^{2}}{49}+\frac{(y-5)^{2}}{4}=1
25x^2+5y^2-20y-216=0	25x^{2}+5y^{2}-20y-216=0
((x-5)^2)/4+((y+2)^2)/1 =1	\frac{(x-5)^{2}}{4}+\frac{(y+2)^{2}}{1}=1
(8x^2-12x+8y^2+20y+17)/8-2=0	\frac{8x^{2}-12x+8y^{2}+20y+17}{8}-2=0
(x^2)/(20)+(y^2)/(25)=1	\frac{x^{2}}{20}+\frac{y^{2}}{25}=1
16x^2+25y^2-32x-100y-284=0	16x^{2}+25y^{2}-32x-100y-284=0
9x^2-54x+4y^2-8y-59=0	9x^{2}-54x+4y^{2}-8y-59=0
((x+5)^2)/(20)+((y-6)^2)/(11)=1	\frac{(x+5)^{2}}{20}+\frac{(y-6)^{2}}{11}=1
x^2-4x+4y^2-8y-4=0	x^{2}-4x+4y^{2}-8y-4=0
x^2+y^2+y^2= 9/4	x^{2}+y^{2}+y^{2}=\frac{9}{4}
(x-0.017)^2+((y^2)/((0.999)^2))=1	(x-0.017)^{2}+(\frac{y^{2}}{(0.999)^{2}})=1
x^2-xy+1/2 (x+y)^2=4	x^{2}-xy+\frac{1}{2}(x+y)^{2}=4
(4x^2-8x)+(9y^2-36y)=-4	(4x^{2}-8x)+(9y^{2}-36y)=-4
2=x^2+4y^2	2=x^{2}+4y^{2}
(x^2)/(1^2)+(y^2)/(sqrt(0.4375)^2)=1	\frac{x^{2}}{1^{2}}+\frac{y^{2}}{\sqrt{0.4375}^{2}}=1
22x^2+66y^2+60x+4y-9=0	22x^{2}+66y^{2}+60x+4y-9=0
x^2+2y^2-5=1	x^{2}+2y^{2}-5=1
(x^2)/(841)+(y^2)/(484)=1	\frac{x^{2}}{841}+\frac{y^{2}}{484}=1
(x^2)/(1.5869^2)+(y^2)/(0.99^2)=1	\frac{x^{2}}{1.5869^{2}}+\frac{y^{2}}{0.99^{2}}=1
(x^2)/(81)+(y^2)/(77)=1	\frac{x^{2}}{81}+\frac{y^{2}}{77}=1
9x^2+18x+25y^2+150y+9=0	9x^{2}+18x+25y^{2}+150y+9=0
((x+3)/2)^2+(y-2)^2= 1/4	(\frac{x+3}{2})^{2}+(y-2)^{2}=\frac{1}{4}
((x-1)^2}{16}+\frac{(y-5)^2)/4 =1	\frac{(x-1)^{2}}{16}+\frac{(y-5)^{2}}{4}=1
9x^2+5y^2+89x-60y=120	9x^{2}+5y^{2}+89x-60y=120
(x^2)/(25)+(y^2)/(81)=1	\frac{x^{2}}{25}+\frac{y^{2}}{81}=1
x/((x^2){64}+\frac{y^2)/9}=1	\frac{x}{\frac{x^{2}}{64}+\frac{y^{2}}{9}}=1
y^2+2x^2=4	y^{2}+2x^{2}=4
x^2+1/4 y^2=x+y	x^{2}+\frac{1}{4}y^{2}=x+y
((x-2)^2}{1^2}+\frac{(y+1)^2)/2 =1	\frac{(x-2)^{2}}{1^{2}}+\frac{(y+1)^{2}}{2}=1
(x^2)/((1)^2)+(y^2)/((1/2)^2)=2	\frac{x^{2}}{(1)^{2}}+\frac{y^{2}}{(\frac{1}{2})^{2}}=2
(x^2)/((1)^2)+(y^2)/((1/2)^2)=1	\frac{x^{2}}{(1)^{2}}+\frac{y^{2}}{(\frac{1}{2})^{2}}=1
((x+3)^2)/(6^2)+((y+7)^2)/(2^2)=1	\frac{(x+3)^{2}}{6^{2}}+\frac{(y+7)^{2}}{2^{2}}=1
25x^{(2)}-200x+y^{(2)}+4y+379=0	25x^{(2)}-200x+y^{(2)}+4y+379=0
((x-0)^2)/(2^2)+((y-0)^2)/(4^2)=1	\frac{(x-0)^{2}}{2^{2}}+\frac{(y-0)^{2}}{4^{2}}=1
77x^2+81y^2-828x-324y=1944	77x^{2}+81y^{2}-828x-324y=1944
(((x+1)^2))/9+(((y+1)^2))/(16)=1	\frac{((x+1)^{2})}{9}+\frac{((y+1)^{2})}{16}=1
55x^2+5y^2=4	55x^{2}+5y^{2}=4
81(x-2)^2+36(y-3)^2=2916	81(x-2)^{2}+36(y-3)^{2}=2916
3x^2+5y^2-6x-20y+8=0	3x^{2}+5y^{2}-6x-20y+8=0
((x+17/2)^2)/(144)+((y+13/2)^2)/(121)=1	\frac{(x+\frac{17}{2})^{2}}{144}+\frac{(y+\frac{13}{2})^{2}}{121}=1
(x^2)/3+(y^2)/(sqrt(5))=1	\frac{x^{2}}{3}+\frac{y^{2}}{\sqrt{5}}=1
0^2=(-sqrt(16-x^2-y^2))^2	0^{2}=(-\sqrt{16-x^{2}-y^{2}})^{2}
150=60x-2x^2+80y-4y^2	150=60x-2x^{2}+80y-4y^{2}
16x^2+25y^2+100y=300	16x^{2}+25y^{2}+100y=300
25x^2+4y^2-50x+8y-71=0	25x^{2}+4y^{2}-50x+8y-71=0
16x^2-64x+25y^2+100y=236	16x^{2}-64x+25y^{2}+100y=236
9x^2+11y^2=10	9x^{2}+11y^{2}=10
16x^2+36y^2+32x+72y-524=0	16x^{2}+36y^{2}+32x+72y-524=0
1/3 3x^2+3y^2-8x-8y*31=0	\frac{1}{3}3x^{2}+3y^{2}-8x-8y\cdot\:31=0
2x^2+3y^2-18=0	2x^{2}+3y^{2}-18=0
49x^2+16y^2-588x+128y+1236=0	49x^{2}+16y^{2}-588x+128y+1236=0
18x^2+24y+12y^2-12x=1	18x^{2}+24y+12y^{2}-12x=1
2x^2+y^2<= 8	2x^{2}+y^{2}\le\:8
x^2+4y^2-12x-16y=48	x^{2}+4y^{2}-12x-16y=48
2x^2+y^2<= 2	2x^{2}+y^{2}\le\:2
(x-3)^2+((y+3)/(16))^2=1	(x-3)^{2}+(\frac{y+3}{16})^{2}=1
(1/4)x^2+y^2= 1/4	(\frac{1}{4})x^{2}+y^{2}=\frac{1}{4}
100x^2+4y^2+1200x-32y+3264=0	100x^{2}+4y^{2}+1200x-32y+3264=0
16x^2+15y^2-64x-90y-41=0	16x^{2}+15y^{2}-64x-90y-41=0
25y^2+9x^2-108x-200y+499=0	25y^{2}+9x^{2}-108x-200y+499=0
50=(100)/(1+x^2+y^2)	50=\frac{100}{1+x^{2}+y^{2}}
9x^2+4y^2-36x+8y+31=0	9x^{2}+4y^{2}-36x+8y+31=0
(x^2)/(1.5869^2)+(y^2)/(0.99898^2)=1	\frac{x^{2}}{1.5869^{2}}+\frac{y^{2}}{0.99898^{2}}=1
9x^2+25y^2+90x=0	9x^{2}+25y^{2}+90x=0
x^2+2y^2=11	x^{2}+2y^{2}=11
3x^2+y^2-5x=2-y	3x^{2}+y^{2}-5x=2-y
((x-3)^2)/4+((y-3)^2)/(16)=1	\frac{(x-3)^{2}}{4}+\frac{(y-3)^{2}}{16}=1
4x^2+2y^2=16	4x^{2}+2y^{2}=16
(x^2)/(1/2)+y^2=1	\frac{x^{2}}{\frac{1}{2}}+y^{2}=1
x^2+4y^2+9x+9y-15=0	x^{2}+4y^{2}+9x+9y-15=0
4x^2+16y^2-8x+96y+84=0	4x^{2}+16y^{2}-8x+96y+84=0
(x^2)/9+(2x)/9+y^2-6y+9=0	\frac{x^{2}}{9}+\frac{2x}{9}+y^{2}-6y+9=0
5x^2+2y^2=45	5x^{2}+2y^{2}=45
((x+3)^2)/(12)+((y-2)^2)/(16)=1	\frac{(x+3)^{2}}{12}+\frac{(y-2)^{2}}{16}=1
2x^2+y^2-2x+3y=5	2x^{2}+y^{2}-2x+3y=5

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