Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 1201 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 1 |
| 1202 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 1203 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 19 }{ 10 } \right)^2}{ \frac{ 209 }{ 10 } } + \dfrac{ \left( y - 3 \right)^2}{ \frac{ 41 }{ 5 } } = 1 $$ | 1 |
| 1204 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 9 }{ 10 } \right)^2}{ 18 } + \dfrac{ \left( y + \frac{ 31 }{ 10 } \right)^2}{ \frac{ 37 }{ 10 } } = 1 $$ | 1 |
| 1205 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 71 }{ 10 } \right)^2}{ \frac{ 3 }{ 2 } } + \dfrac{ \left( y - \frac{ 49 }{ 5 } \right)^2}{ \frac{ 3 }{ 10 } } = 1 $$ | 1 |
| 1206 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 24 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 1207 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \sqrt{ 60 } } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
| 1208 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 60 } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
| 1209 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 5y^2 = 25 $$ | 1 |
| 1210 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + 4y^2 = 100 $$ | 1 |
| 1211 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ \frac{ 22 }{ 5 } } + \dfrac{ \left( y - 4 \right)^2}{ 2 } = 1 $$ | 1 |
| 1212 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 81 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 1213 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 308 } + \dfrac{ y^2}{ 200 } = 1 $$ | 1 |
| 1214 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 200 } + \dfrac{ y^2}{ 308 } = 1 $$ | 1 |
| 1215 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 15x^2 + 10y^2 = 1 $$ | 1 |
| 1216 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 12y^2 = 108 $$ | 1 |
| 1217 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 441 } + \dfrac{ y^2}{ 144 } = 1 $$ | 1 |
| 1218 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 147 }{ 2 } \right)^2}{ 6 } + \dfrac{ \left( y - 27 \right)^2}{ \frac{ 1 }{ 100 } } = 1 $$ | 1 |
| 1219 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 6 } = 1 $$ | 1 |
| 1220 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 5 } = 1 $$ | 1 |
| 1221 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 2 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 1222 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 32 } + \dfrac{ y^2}{ 5 } = 1 $$ | 1 |
| 1223 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 1224 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 1225 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ \left( y - 2 \right)^2}{ 36 } = 1 $$ | 1 |
| 1226 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 16 } + \dfrac{ \left( y - 3 \right)^2}{ 4 } = 1 $$ | 1 |
| 1227 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 6 } = 1 $$ | 1 |
| 1228 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 32 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 1229 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 32 } + \dfrac{ y^2}{ 8 } = 1 $$ | 1 |
| 1230 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 32 } + \dfrac{ y^2}{ 10 } = 1 $$ | 1 |
| 1231 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 11 }{ 25 } \right)^2}{ \frac{ 243 }{ 100 } } + \dfrac{ \left( y - \frac{ 1 }{ 10 } \right)^2}{ \frac{ 167 }{ 50 } } = 1 $$ | 1 |
| 1232 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 12 } = 1 $$ | 1 |
| 1233 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 11979 }{ 25 } } + \dfrac{ y^2}{ 230 } = 1 $$ | 1 |
| 1234 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 29 } + \dfrac{ y^2}{ \frac{ 327 }{ 5 } } = 1 $$ | 1 |
| 1235 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 49 } + \dfrac{ \left( y + 5 \right)^2}{ 25 } = 1 $$ | 1 |
| 1236 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 25 } + \dfrac{ \left( y - 1 \right)^2}{ 144 } = 1 $$ | 1 |
| 1237 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 31 }{ 10 } } + \dfrac{ \left( y + \frac{ 17 }{ 10 } \right)^2}{ \frac{ 8 }{ 5 } } = 1 $$ | 1 |
| 1238 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 1 |
| 1239 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 4y^2 = 25 $$ | 1 |
| 1240 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 12x^2 + 9y^2 = 36 $$ | 1 |
| 1241 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ \left( y + 2 \right)^2}{ 1 } = 1 $$ | 1 |
| 1242 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + 9y^2 = 36 $$ | 1 |
| 1243 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 1 |
| 1244 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 8836 } + \dfrac{ y^2}{ 3844 } = 1 $$ | 1 |
| 1245 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 3 } + \dfrac{ \left( y + 1 \right)^2}{ 2 } = 1 $$ | 1 |
| 1246 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 5 } + \dfrac{ y^2}{ \frac{ 11 }{ 2 } } = 1 $$ | 1 |
| 1247 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ \frac{ 121 }{ 4 } } = 1 $$ | 1 |
| 1248 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 1 |
| 1249 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y + 1 \right)^2}{ 6 } = 1 $$ | 1 |
| 1250 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + y^2 = 25 $$ | 1 |
