Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 251 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 25 } + \dfrac{ \left( y + 3 \right)^2}{ 4 } = 1 $$ | 3 |
| 252 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 9 } + \dfrac{ \left( y + 4 \right)^2}{ 4 } = 1 $$ | 3 |
| 253 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 11 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y - 1 \right)^2}{ 5 } = 1 $$ | 3 |
| 254 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 1 \right)^2}{ \frac{ 1 }{ 5 } } = 1 $$ | 3 |
| 255 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y - 1 \right)^2}{ 5 } = 1 $$ | 3 |
| 256 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 1 \right)^2}{ 5 } = 1 $$ | 3 |
| 257 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 9 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 1 \right)^2}{ 5 } = 1 $$ | 3 |
| 258 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 11 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 1 \right)^2}{ 5 } = 1 $$ | 3 |
| 259 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 22 }{ 25 } \right)^2}{ \frac{ 1 }{ 200 } } + \dfrac{ \left( y - \frac{ 73 }{ 10 } \right)^2}{ \frac{ 11 }{ 500 } } = 1 $$ | 3 |
| 260 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 3 } + \dfrac{ y^2}{ 9 } = 1 $$ | 3 |
| 261 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 4 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 3 |
| 262 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 10 \right)^2}{ 81 } + \dfrac{ \left( y - 1 \right)^2}{ 1 } = 1 $$ | 3 |
| 263 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 5 } + \dfrac{ y^2}{ 4 } = 1 $$ | 3 |
| 264 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 15 } + \dfrac{ y^2}{ 30 } = 1 $$ | 3 |
| 265 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 25 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 3 |
| 266 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 25 } + \dfrac{ \left( y + 3 \right)^2}{ 16 } = 1 $$ | 3 |
| 267 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 5 } = 1 $$ | 3 |
| 268 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 36 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 3 |
| 269 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 100 } + \dfrac{ \left( y - 6 \right)^2}{ 1 } = 1 $$ | 3 |
| 270 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 36 } = 1 $$ | 3 |
| 271 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 49 } = 1 $$ | 3 |
| 272 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 9 \right)^2}{ 121 } + \dfrac{ \left( y - 8 \right)^2}{ 16 } = 1 $$ | 3 |
| 273 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 16x^2 + 49y^2 = 784 $$ | 3 |
| 274 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 3 |
| 275 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 25 } + \dfrac{ \left( y + 4 \right)^2}{ 9 } = 1 $$ | 3 |
| 276 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 100 } + \dfrac{ y^2}{ 400 } = 1 $$ | 3 |
| 277 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 14 } + \dfrac{ y^2}{ 9 } = 1 $$ | 3 |
| 278 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 8 \right)^2}{ 25 } + \dfrac{ \left( y - 7 \right)^2}{ 49 } = 1 $$ | 3 |
| 279 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y + 5 \right)^2}{ 4 } = 1 $$ | 3 |
| 280 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 3 |
| 281 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 2y^2 = 6 $$ | 3 |
| 282 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 8 } = 1 $$ | 3 |
| 283 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 16 } = 1 $$ | 3 |
| 284 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 3 |
| 285 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 25 } + \dfrac{ \left( y - 1 \right)^2}{ 16 } = 1 $$ | 3 |
| 286 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 7 \right)^2}{ 9 } + \dfrac{ \left( y + 3 \right)^2}{ 49 } = 1 $$ | 3 |
| 287 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 25 } = 1 $$ | 3 |
| 288 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 16 } = 1 $$ | 3 |
| 289 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 5x^2 + 2y^2 = 20 $$ | 2 |
| 290 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 5x^2 + 9y^2 = 45 $$ | 2 |
| 291 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 4 \left( x - 1 \right)^2}{ \frac{ 3 }{ 2 } } + \dfrac{ \left( y - 2 \right)^2}{ 3 } = 1 $$ | 2 |
| 292 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 17 }{ 10 } \right)^2}{ 6 } + \dfrac{ y^2}{ 15 } = 1 $$ | 2 |
| 293 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 17 }{ 10 } \right)^2}{ 6 } + \dfrac{ y^2}{ 15 } = 1 $$ | 2 |
| 294 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 7 }{ 2 } \right)^2}{ 4 } + \dfrac{ \left( y + \frac{ 5 }{ 2 } \right)^2}{ 2 } = 1 $$ | 2 |
| 295 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 5x^2 + y^2 = 5 $$ | 2 |
| 296 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 1 } + \dfrac{ \left( y + 3 \right)^2}{ 4 } = 1 $$ | 2 |
| 297 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 10 \right)^2}{ \frac{ 11 }{ 2 } } + \dfrac{ \left( y - 1 \right)^2}{ 3 } = 1 $$ | 2 |
| 298 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 10 \right)^2}{ 121 } + \dfrac{ \left( y + 7 \right)^2}{ 49 } = 1 $$ | 2 |
| 299 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 181 }{ 10 } } + \dfrac{ y^2}{ \frac{ 91 }{ 10 } } = 1 $$ | 2 |
| 300 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y - 5 \right)^2}{ 9 } = 1 $$ | 2 |
