Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 201 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 12 } + \dfrac{ \left( y + 4 \right)^2}{ 36 } = 1 $$ | 4 |
| 202 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2350 } + \dfrac{ y^2}{ 1550 } = 1 $$ | 4 |
| 203 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 900 } + \dfrac{ y^2}{ 500 } = 1 $$ | 4 |
| 204 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 400 } + \dfrac{ y^2}{ 256 } = 1 $$ | 4 |
| 205 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 18 } + \dfrac{ y^2}{ 10 } = 1 $$ | 4 |
| 206 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 13 } = 1 $$ | 3 |
| 207 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 17 } + \dfrac{ y^2}{ 1 } = 1 $$ | 3 |
| 208 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 36 } + \dfrac{ \left( y + 2 \right)^2}{ 100 } = 1 $$ | 3 |
| 209 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 3 |
| 210 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 64 } + \dfrac{ \left( y - 2 \right)^2}{ 25 } = 1 $$ | 3 |
| 211 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 121 } = 1 $$ | 3 |
| 212 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y - 5 \right)^2}{ 9 } = 1 $$ | 3 |
| 213 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 7 } + \dfrac{ y^2}{ 4 } = 1 $$ | 3 |
| 214 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 9y^2 = 36 $$ | 3 |
| 215 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 10 } + \dfrac{ y^2}{ 5 } = 1 $$ | 3 |
| 216 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 57 }{ 20 } \right)^2}{ 1 } + \dfrac{ \left( y - \frac{ 51 }{ 25 } \right)^2}{ \frac{ 3 }{ 5 } } = 1 $$ | 3 |
| 217 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 32 } + \dfrac{ y^2}{ 4 } = 1 $$ | 3 |
| 218 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 36 } = 1 $$ | 3 |
| 219 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 25 } + \dfrac{ \left( y + 3 \right)^2}{ 4 } = 1 $$ | 3 |
| 220 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 75 } + \dfrac{ y^2}{ 61 } = 1 $$ | 3 |
| 221 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 64 } = 1 $$ | 3 |
| 222 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 3 } = 1 $$ | 3 |
| 223 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ 4 } = 1 $$ | 3 |
| 224 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 48 } = 1 $$ | 3 |
| 225 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 39 } = 1 $$ | 3 |
| 226 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 9 } + \dfrac{ y^2}{ 3 } = 1 $$ | 3 |
| 227 | 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 |
| 228 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 40 } + \dfrac{ y^2}{ 30 } = 1 $$ | 3 |
| 229 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 16 } = 1 $$ | 3 |
| 230 | 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 |
| 231 | 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 |
| 232 | 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 |
| 233 | 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 |
| 234 | 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 |
| 235 | 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 |
| 236 | 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 |
| 237 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 2y^2 = 6 $$ | 3 |
| 238 | 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 |
| 239 | 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 |
| 240 | 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 |
| 241 | 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 |
| 242 | 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 |
| 243 | 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 |
| 244 | 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 |
| 245 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 16x^2 + 49y^2 = 784 $$ | 3 |
| 246 | 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 |
| 247 | 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 |
| 248 | 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 |
| 249 | 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 |
| 250 | 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 |
