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Problemas populares de Geometry

x^2+4y^2-20x+84=0	x^{2}+4y^{2}-20x+84=0
(x^2+y^2-16x+8y+80)=4(x^2+y^2-4x-8y+20)	(x^{2}+y^{2}-16x+8y+80)=4(x^{2}+y^{2}-4x-8y+20)
16(x-2)^2+25(y+3)^2=124	16(x-2)^{2}+25(y+3)^{2}=124
3x^2+y^2+12x-2y+1=0	3x^{2}+y^{2}+12x-2y+1=0
10y^2+x^2=5	10y^{2}+x^{2}=5
9x^2+4(y-2)^2=36	9x^{2}+4(y-2)^{2}=36
((x-4)^2)/(5^2)+((y-1)^2)/(2^2)=1	\frac{(x-4)^{2}}{5^{2}}+\frac{(y-1)^{2}}{2^{2}}=1
1x^2+4y^2+10x+8y-19=0	1x^{2}+4y^{2}+10x+8y-19=0
36x^2+9y^2+288x-90y+477=0	36x^{2}+9y^{2}+288x-90y+477=0
((x^2)/(72))+((y^2)/(21))=1	(\frac{x^{2}}{72})+(\frac{y^{2}}{21})=1
(3-y^2-3x^2)=0	(3-y^{2}-3x^{2})=0
((x-4)^2)/9+((y-7)^2)/(36)=1	\frac{(x-4)^{2}}{9}+\frac{(y-7)^{2}}{36}=1
(((x-2)^2))/((9))+(((y+5)^2))/((25))=1	\frac{((x-2)^{2})}{(9)}+\frac{((y+5)^{2})}{(25)}=1
16x^2+25y^2=1400	16x^{2}+25y^{2}=1400
5x^2+9y^2-80x+54y+221=0	5x^{2}+9y^{2}-80x+54y+221=0
(x/(16))^2+(y^2)/(81)=1	(\frac{x}{16})^{2}+\frac{y^{2}}{81}=1
11x^2+5y^2+110x-20y+240=0	11x^{2}+5y^{2}+110x-20y+240=0
(x^2)/(cosh^2(β))+(y^2)/(sinh^2(β))=1	\frac{x^{2}}{\cosh^{2}(β)}+\frac{y^{2}}{\sinh^{2}(β)}=1
4x^2=36-9y^2	4x^{2}=36-9y^{2}
((x+2)^2)/(25)+((y-1)^2)/(16)=1	\frac{(x+2)^{2}}{25}+\frac{(y-1)^{2}}{16}=1
25x^2+16y^2+100x-96y-154=0	25x^{2}+16y^{2}+100x-96y-154=0
((x+1)^2)/(25)+((y+5)^2)/(16)=1	\frac{(x+1)^{2}}{25}+\frac{(y+5)^{2}}{16}=1
49x^2+25y^2-1225=0	49x^{2}+25y^{2}-1225=0
15x^2+12y^2+30x-24y=150	15x^{2}+12y^{2}+30x-24y=150
2x^2+5y^2-4x+y-6=0	2x^{2}+5y^{2}-4x+y-6=0
30x^2+9y^2=225	30x^{2}+9y^{2}=225
3x^2+8y^2=1	3x^{2}+8y^{2}=1
((x-2.63)^2)/(1.34)+(y^2)/(3.22)-1=1	\frac{(x-2.63)^{2}}{1.34}+\frac{y^{2}}{3.22}-1=1
4x^2+y^2-32x-80=0	4x^{2}+y^{2}-32x-80=0
(x-2/3)^2+4(y-1)^2=4	(x-\frac{2}{3})^{2}+4(y-1)^{2}=4
2x^2+x+y^2-6=0	2x^{2}+x+y^{2}-6=0
(4x)/(x^2+y^2)=-2	\frac{4x}{x^{2}+y^{2}}=-2
y^2+4x^2+24x+16y=-84	y^{2}+4x^{2}+24x+16y=-84
(y^2}{10}+\frac{x^2)/6 =1	\frac{y^{2}}{10}+\frac{x^{2}}{6}=1
x^2-8x+2y^2+8y=20	x^{2}-8x+2y^{2}+8y=20
x^2+36y^2-24x-288y+611=0	x^{2}+36y^{2}-24x-288y+611=0
169x^2+25y^2=4225	169x^{2}+25y^{2}=4225
3x^2+4y^2+28x-16y+48=0	3x^{2}+4y^{2}+28x-16y+48=0
6x^2+y^2-12x+2y=1	6x^{2}+y^{2}-12x+2y=1
(x-5)^2+(y+8)^2+(x-3)^2-98=0	(x-5)^{2}+(y+8)^{2}+(x-3)^{2}-98=0
5x^2+9y^2+30x=0	5x^{2}+9y^{2}+30x=0
4x^2+7y^2=28	4x^{2}+7y^{2}=28
5u^2-4u+v^2+2v=0	5u^{2}-4\cdot\:u+v^{2}+2\cdot\:v=0
3x^2+2y^2-6x-12y+15=0	3x^{2}+2y^{2}-6x-12y+15=0
9y^2+x^2=9	9y^{2}+x^{2}=9
4x^2+7y^2-140=0	4x^{2}+7y^{2}-140=0
x^2+5y^2-30y+25=0	x^{2}+5y^{2}-30y+25=0
3x^2+9y^2-6x-7y-8=0	3x^{2}+9y^{2}-6x-7y-8=0
(x^2)/(25)+(y^2)/(39)=1	\frac{x^{2}}{25}+\frac{y^{2}}{39}=1
x^2=6y-y^2	x^{2}=6y-y^{2}
((x-81)^2)/(64^2)+((y-64)^2)/(81^2)=1	\frac{(x-81)^{2}}{64^{2}}+\frac{(y-64)^{2}}{81^{2}}=1
((x-4)^2)/1+((y+9)^2)/9 =1	\frac{(x-4)^{2}}{1}+\frac{(y+9)^{2}}{9}=1
solvefor x,2^2=h(x)^2+(x/2)^2	solvefor\:x,2^{2}=h(x)^{2}+(\frac{x}{2})^{2}
4x^2+y^2<= 17	4x^{2}+y^{2}\le\:17
0.5=4x^2+y^2	0.5=4x^{2}+y^{2}
(x^2)/9+y^2>9	\frac{x^{2}}{9}+y^{2}>9
((x+8)^2)/(20)+((y+36)^2)/(36)=1	\frac{(x+8)^{2}}{20}+\frac{(y+36)^{2}}{36}=1
4x^2+y^2-16x-2y+1=0	4x^{2}+y^{2}-16x-2y+1=0
5x^2+z^2=100	5x^{2}+z^{2}=100
((x+2)^2)/(16)+((y+3)^2)/(36)=1	\frac{(x+2)^{2}}{16}+\frac{(y+3)^{2}}{36}=1
(25x^2)/(400-12^2)+(16y^2)/(400-12^2)=1	\frac{25x^{2}}{400-12^{2}}+\frac{16y^{2}}{400-12^{2}}=1
(x^2)/(81)+(y^2)/(225)=1	\frac{x^{2}}{81}+\frac{y^{2}}{225}=1
((x+2)^2)/(16)+((y-4)^2)/(25)=1	\frac{(x+2)^{2}}{16}+\frac{(y-4)^{2}}{25}=1
((x-3)^2)/(169)+((y+4)^2)/(144)=1	\frac{(x-3)^{2}}{169}+\frac{(y+4)^{2}}{144}=1
9x^2+7y^2=42	9x^{2}+7y^{2}=42
((x-2.1)^2)/(2.25)+((y+1.6)^2)/(6.16)=1	\frac{(x-2.1)^{2}}{2.25}+\frac{(y+1.6)^{2}}{6.16}=1
x^2-2x+3y^2-2y-5=0	x^{2}-2x+3y^{2}-2y-5=0
((x-5)^2)/(8^2)+((y+2)^2)/(10^2)=1	\frac{(x-5)^{2}}{8^{2}}+\frac{(y+2)^{2}}{10^{2}}=1
2y-x^2-y^2>= 0	2y-x^{2}-y^{2}\ge\:0
25x^2+4y^2-8x+200y+304=0	25x^{2}+4y^{2}-8x+200y+304=0
2x^2+y^2+2y=1	2x^{2}+y^{2}+2y=1
(x^2}{25}+\frac{(y-2)^2)/4 =1	\frac{x^{2}}{25}+\frac{(y-2)^{2}}{4}=1
y-3=-x/(4y)(x-12)	y-3=-\frac{x}{4y}(x-12)
4x^2-34y+13y^2-36=0	4x^{2}-34y+13y^{2}-36=0
5x^2+2y^2+12y=-8	5x^{2}+2y^{2}+12y=-8
((x+7)^2}{16}+\frac{(y+5)^2)/4 =1	\frac{(x+7)^{2}}{16}+\frac{(y+5)^{2}}{4}=1
x^2+3*y^2=84	x^{2}+3\cdot\:y^{2}=84
y^2=9-4x^2	y^{2}=9-4x^{2}
25x^2+16y^2-150x+64y=111	25x^{2}+16y^{2}-150x+64y=111
(x^2}{25}+\frac{y^2)/1 =1	\frac{x^{2}}{25}+\frac{y^{2}}{1}=1
(x^2)/(27^2)+(y^2)/(25^2)=1	\frac{x^{2}}{27^{2}}+\frac{y^{2}}{25^{2}}=1
1-x^2=(y^2)/4	1-x^{2}=\frac{y^{2}}{4}
(2x)/(x^2+2y^2)=2	\frac{2x}{x^{2}+2y^{2}}=2
(x^2)/(3^2)+(y^2)/(7^2)=1	\frac{x^{2}}{3^{2}}+\frac{y^{2}}{7^{2}}=1
-y^2-z^2=1	-y^{2}-z^{2}=1
((x-5)^2)/4+((y+2)^2)/2 =1	\frac{(x-5)^{2}}{4}+\frac{(y+2)^{2}}{2}=1
6x^2+144y^2=864	6x^{2}+144y^{2}=864
((x-(-1))^2)/(4^2)+((y-(-1))^2)/(3^2)=1	\frac{(x-(-1))^{2}}{4^{2}}+\frac{(y-(-1))^{2}}{3^{2}}=1
81x^2+9y^2=64	81x^{2}+9y^{2}=64
y^2+30x^2=30	y^{2}+30x^{2}=30
vértices (x^2)/(25)+((y+3)^2)/(49)=1	vertices\:\frac{x^{2}}{25}+\frac{(y+3)^{2}}{49}=1
vértices 9x^2+25y^2=225	vertices\:9x^{2}+25y^{2}=225
vértices 81x^2-1296x+16y^2+64y=-3952	vertices\:81x^{2}-1296x+16y^{2}+64y=-3952
vértices 6x^2+8y^2+12x-32y=178	vertices\:6x^{2}+8y^{2}+12x-32y=178
vértices 49x^2+25y^2-196x+250y-404=0	vertices\:49x^{2}+25y^{2}-196x+250y-404=0
vértices ((x-3)^2)/(49)+((y+5)^2)/(25)=1	vertices\:\frac{(x-3)^{2}}{49}+\frac{(y+5)^{2}}{25}=1
vértices (x^2)/(64)+(y^2)/(100)=1	vertices\:\frac{x^{2}}{64}+\frac{y^{2}}{100}=1
vértices x^2+(y^2)/(49)=1	vertices\:x^{2}+\frac{y^{2}}{49}=1
vértices 4x^2+9y^2-16x+18y-11=0	vertices\:4x^{2}+9y^{2}-16x+18y-11=0
vértices (x^2)/(16)+(y^2)/(12)=1	vertices\:\frac{x^{2}}{16}+\frac{y^{2}}{12}=1

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