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בעיות גאומטריה פופולריות

vertices (x^2}{25}+\frac{y^2)/9 =1	`vertices` `x`²25 +`y`²9 =1
x^2-(y^2)/(16)=1	`x`²−`y`²16 =1
vertices 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
axis x^2-6x+5y=-34	`axis` `x`²−6`x`+5`y`=−34
vertices f(x)=x^2-2x-3	`vertices` `f`(`x`)=`x`²−2`x`−3
y+x^2=4x	`y`+`x`²=4`x`
asymptotes (x^2}{36}-\frac{y^2)/9 =1	`asymptotes` `x`²36 −`y`²9 =1
directrix x^2=8y	`directrix` `x`²=8`y`
foci y^2=32x	`foci` `y`²=32`x`
foci 16x^2-9y^2=144	`foci` 16`x`²−9`y`²=144
vertices 3x^2+y^2+18x-2y-8=0	`vertices` 3`x`²+`y`²+18`x`−2`y`−8=0
directrix x^2=12y	`directrix` `x`²=12`y`
x^2+y^2-6x+4y+4=0	`x`²+`y`²−6`x`+4`y`+4=0
directrix y= 1/2 x^2	`directrix` `y`=12 `x`²
foci (y^2)/9-(x^2)/4 =1	`foci` `y`²9 −`x`²4 =1
x^2=3y	`x`²=3`y`
(a+1)/b =(a-1)/b+(b+1)/a	`a`+1`b` =`a`−1`b` +`b`+1`a`
foci (x^2)/4+(y^2)/9 =1	`foci` `x`²4 +`y`²9 =1
directrix y^2-y-x+1=0	`directrix` `y`²−`y`−`x`+1=0
((x-5)^2)/4+((y+3)^2)/(16)=1	(`x`−5)²4 +(`y`+3)²16 =1
x^2=6y	`x`²=6`y`
foci ((y-3)^2}{11}-\frac{(x+1)^2)/5 =1	`foci` (`y`−3)²11 −(`x`+1)²5 =1
x^2+2x+y^2+4y=20	`x`²+2`x`+`y`²+4`y`=20
x-y^2=0	`x`−`y`²=0
x^2+y^2-4x=0	`x`²+`y`²−4`x`=0
x^2+y^2-2x-4y+1=0	`x`²+`y`²−2`x`−4`y`+1=0
4x^2-y^2-24x-4y+28=0	4`x`²−`y`²−24`x`−4`y`+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+10`x`−4`y`−7=0
foci y^2=-10x	`foci` `y`²=−10`x`
x^2=8y	`x`²=8`y`
foci (x+6)^2+((y+4)^2)/(1/4)=1	`foci` (`x`+6)²+(`y`+4)²14 =1
(x^2)/(25)+(y^2)/(16)=1	`x`²25 +`y`²16 =1
vertices (y^2)/(36)-(x^2)/(64)=1	`vertices` `y`²36 −`x`²64 =1
x^2+(y+2)^2=4	`x`²+(`y`+2)²=4
x=4y^2+8y-3	`x`=4`y`²+8`y`−3
(x^2)/(16)+y^2=1	`x`²16 +`y`²=1
y^2=-20x	`y`²=−20`x`
x^2-4x-8y+2=0	`x`²−4`x`−8`y`+2=0
3x^2-15y^2+2x-3y=4	3`x`²−15`y`²+2`x`−3`y`=4
x^2+y^2=3	`x`²+`y`²=3
vertices (x-12)^2-156	`vertices` (`x`−12)²−156
foci y^2=-4x	`foci` `y`²=−4`x`
directrix y^2=4x	`directrix` `y`²=4`x`
directrix (y-7)^2=-12(x+1)	`directrix` (`y`−7)²=−12(`x`+1)
foci x^2=-16y	`foci` `x`²=−16`y`
foci x^2	`foci` `x`²
foci ((x-3)^2)/5+((y-1)^2)/(15)=1	`foci` (`x`−3)²5 +(`y`−1)²15 =1
foci (x^2)/(100)+(y^2)/(64)=1	`foci` `x`²100 +`y`²64 =1
foci (x^2)/4+(y^2)/(16)=1	`foci` `x`²4 +`y`²16 =1
foci 3x^2+2y^2=6	`foci` 3`x`²+2`y`²=6
vertices (x^2}{25}+\frac{y^2)/4 =1	`vertices` `x`²25 +`y`²4 =1
4x^2+y^2=16	4`x`²+`y`²=16
foci y^2=-8x	`foci` `y`²=−8`x`
x=y^2-5	`x`=`y`²−5
vertices y=x^2+2x-3	`vertices` `y`=`x`²+2`x`−3
(x^2)/(25)+(y^2)/(36)=1	`x`²25 +`y`²36 =1
vertices 2x^2	`vertices` 2`x`²
foci 4y^2-25x^2=100	`foci` 4`y`²−25`x`²=100
-9x^2+y^2-72x-153=0	−9`x`²+`y`²−72`x`−153=0
vertices f(x)=x^2-2x-15	`vertices` `f`(`x`)=`x`²−2`x`−15
x^2-9y^2=9	`x`²−9`y`²=9
foci (x^2)/(36)+(y^2)/(100)=1	`foci` `x`²36 +`y`²100 =1
vertices f(x)=-x^2-2x+3	`vertices` `f`(`x`)=−`x`²−2`x`+3
x^2+y^2=4	`x`²+`y`²=4
9y^2-16x^2-256=0	9`y`²−16`x`²−256=0
(x^2)/(25)-(y^2)/(36)=1	`x`²25 −`y`²36 =1
-x^2-6x+y-8=0	−`x`²−6`x`+`y`−8=0
x^2+y^2-2x+4y-4=0	`x`²+`y`²−2`x`+4`y`−4=0
directrix x=-1/12 y^2	`directrix` `x`=−112 `y`²
4x^2+9y^2-16x+18y=11	4`x`²+9`y`²−16`x`+18`y`=11
(x^2)/4+(y^2)/1 =1	`x`²4 +`y`²1 =1
vertices x^2	`vertices` `x`²
foci y^2=-12x	`foci` `y`²=−12`x`
9x^2-y^2-36x-6y+18=0	9`x`²−`y`²−36`x`−6`y`+18=0
9y^2-16x^2=144	9`y`²−16`x`²=144
(x-1)^2+y^2=1	(`x`−1)²+`y`²=1
foci 16x^2+25y^2=400	`foci` 16`x`²+25`y`²=400
vertices (x^2)/(25)+(y^2)/(16)=1	`vertices` `x`²25 +`y`²16 =1
4<=-x^2-y	4≤ −`x`²−`y`
18x^2-64x-14y+150=0	18`x`²−64`x`−14`y`+150=0
x^2+y^2+6x-4y-12=0	`x`²+`y`²+6`x`−4`y`−12=0
eccentricity 36x^2+y^2=36	`eccentricity` 36`x`²+`y`²=36
x^2-4x+y^2+6y-12=0	`x`²−4`x`+`y`²+6`y`−12=0
(x^2}{16}+\frac{y^2)/4 =1	`x`²16 +`y`²4 =1
directrix x^2=-4y	`directrix` `x`²=−4`y`
y^2=4-x^2	`y`²=4−`x`²
asymptotes (x^2)/4-(y^2)/4 =1	`asymptotes` `x`²4 −`y`²4 =1
axis (x^2)/9-(y^2)/4 =1	`axis` `x`²9 −`y`²4 =1
foci (y^2)/(36)-(x^2)/(64)=1	`foci` `y`²36 −`x`²64 =1
x=y-y^2	`x`=`y`−`y`²
y^2-8x=0	`y`²−8`x`=0
x^2-2x+y^2+2y=7	`x`²−2`x`+`y`²+2`y`=7
foci (y^2)/(49)-(x^2)/(64)=1	`foci` `y`²49 −`x`²64 =1
solvefor y,36x^2-25y^2+144x-50y+119=0	`solvefor` `y`,36`x`²−25`y`²+144`x`−50`y`+119=0
asymptotes (x^2)/(100)-(y^2)/(64)=1	`asymptotes` `x`²100 −`y`²64 =1
x^2+y^2<= 4	`x`²+`y`²≤ 4
vertices f(x)=x^2+4x+3	`vertices` `f`(`x`)=`x`²+4`x`+3
directrix y= 1/12 x^2	`directrix` `y`=112 `x`²

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