Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 301 | 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 |
| 302 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 7 }{ 2 } \right)^2}{ \frac{ 11 }{ 2 } } + \dfrac{ \left( y - 1 \right)^2}{ 3 } = 1 $$ | 3 |
| 303 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y - 3 \right)^2}{ 36 } = 1 $$ | 3 |
| 304 | 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 |
| 305 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 36 } + \dfrac{ \left( y + 3 \right)^2}{ 12 } = 1 $$ | 3 |
| 306 | 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 |
| 307 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 7 }{ 2 } \right)^2}{ 4 } + \dfrac{ \left( y + \frac{ 5 }{ 2 } \right)^2}{ 2 } = 1 $$ | 3 |
| 308 | 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 |
| 309 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 4 } = 1 $$ | 3 |
| 310 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 0.9573y^2 = 1 $$ | 2 |
| 311 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 1 } + \dfrac{ \left( y + 1 \right)^2}{ 81 } = 1 $$ | 2 |
| 312 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 8x^2 + \frac{ 37 }{ 10 }y^2 = 1 $$ | 2 |
| 313 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 20x^2 + 25y^2 = 1 $$ | 2 |
| 314 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 5 }{ 2 } } + \dfrac{ y^2}{ 2 } = 1 $$ | 2 |
| 315 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 15 \right)^2}{ 2 } + \dfrac{ \left( y + 2 \right)^2}{ 2 } = 1 $$ | 2 |
| 316 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 40 \right)^2}{ 900 } + \dfrac{ \left( y - 40 \right)^2}{ 1600 } = 1 $$ | 2 |
| 317 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 15 \right)^2}{ 3600 } + \dfrac{ \left( y - 30 \right)^2}{ 900 } = 1 $$ | 2 |
| 318 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 10 \right)^2}{ 1600 } + \dfrac{ \left( y - 20 \right)^2}{ 400 } = 1 $$ | 2 |
| 319 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 2 |
| 320 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 25 } + \dfrac{ \left( y - 4 \right)^2}{ 4 } = 1 $$ | 2 |
| 321 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 4 } + \dfrac{ \left( y - 1 \right)^2}{ 1 } = 1 $$ | 2 |
| 322 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 1 }{ 5 } \right)^2}{ 17.1395 } + \dfrac{ \left( y + \frac{ 1 }{ 10 } \right)^2}{ 7.3495 } = 1 $$ | 2 |
| 323 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ \frac{ 191 }{ 2 } } + \dfrac{ \left( y - 1 \right)^2}{ 75 } = 1 $$ | 2 |
| 324 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ \left( y + 1 \right)^2}{ 3 } = 1 $$ | 2 |
| 325 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ y^2}{ 1 } = 1 $$ | 2 |
| 326 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 3x^2 + 4y^2 = 1 $$ | 2 |
| 327 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 9 \left( x - 1 \right)^2}{ 225 } + \dfrac{ 25 \left( y + 2 \right)^2}{ 225 } = 1 $$ | 2 |
| 328 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 10 } + \dfrac{ \left( y + 2 \right)^2}{ 4 } = 1 $$ | 2 |
| 329 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 154 } + \dfrac{ y^2}{ 62 } = 1 $$ | 2 |
| 330 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y - 1 \right)^2}{ 3 } = 1 $$ | 2 |
| 331 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 3 } = 1 $$ | 2 |
| 332 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 2 |
| 333 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 49 } = 1 $$ | 2 |
| 334 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 8640.632 } + \dfrac{ y^2}{ 8637.8436 } = 1 $$ | 2 |
| 335 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 1 \right)^2}{ \frac{ 1 }{ 5 } } = 1 $$ | 2 |
| 336 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ \frac{ 1 }{ 2 } } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 2 |
| 337 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 780 } + \dfrac{ y^2}{ 450 } = 1 $$ | 2 |
| 338 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 59 } + \dfrac{ y^2}{ 64 } = 1 $$ | 2 |
| 339 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 2 |
| 340 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 2 |
| 341 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1156 } + \dfrac{ y^2}{ 900 } = 1 $$ | 2 |
| 342 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ \sqrt{ 8 } } = 1 $$ | 2 |
| 343 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 10 } + \dfrac{ \left( y + 8 \right)^2}{ 15 } = 1 $$ | 2 |
| 344 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 100 } + \dfrac{ y^2}{ \frac{ 121 }{ 4 } } = 1 $$ | 2 |
| 345 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 25 } = 1 $$ | 2 |
| 346 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 9 } + \dfrac{ \left( y + 4 \right)^2}{ 4 } = 1 $$ | 2 |
| 347 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 81 } + \dfrac{ \left( y + 6 \right)^2}{ 49 } = 1 $$ | 2 |
| 348 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 21 \right)^2}{ 1 } + \dfrac{ \left( y - 12 \right)^2}{ 11 } = 1 $$ | 2 |
| 349 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 2 |
| 350 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 144 } + \dfrac{ \left( y - 4 \right)^2}{ 1 } = 1 $$ | 2 |
