Ellipse – Solved Problems Database
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:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 9 } = 1 $$ | 2 |
202 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 100x^2 + 196y^2 = 1225 $$ | 2 |
203 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 12 } + \dfrac{ \left( y + 6 \right)^2}{ 11 } = 1 $$ | 2 |
204 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ 5 } = 1 $$ | 2 |
205 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 5 } = 1 $$ | 2 |
206 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 25 } + \dfrac{ \left( y + 1 \right)^2}{ 64 } = 1 $$ | 2 |
207 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 10 } = 1 $$ | 2 |
208 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 64 } + \dfrac{ \left( y + 1 \right)^2}{ 25 } = 1 $$ | 2 |
209 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 81 } + \dfrac{ \left( y + 9 \right)^2}{ 16 } = 1 $$ | 2 |
210 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 36 } = 1 $$ | 2 |
211 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 49 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 2 |
212 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 8 \right)^2}{ 64 } + \dfrac{ \left( y - 1 \right)^2}{ 49 } = 1 $$ | 2 |
213 | 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 |
214 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 49 } = 1 $$ | 2 |
215 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 49 } + \dfrac{ \left( y - 3 \right)^2}{ 9 } = 1 $$ | 2 |
216 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 100 } + \dfrac{ y^2}{ 36 } = 1 $$ | 2 |
217 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 6y^2 = 18 $$ | 2 |
218 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 36 } + \dfrac{ \left( y - 9 \right)^2}{ 49 } = 1 $$ | 2 |
219 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 7 \right)^2}{ 1 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 2 |
220 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 32 }{ 5 } \right)^2}{ \frac{ 1 }{ 2 } } + \dfrac{ \left( y - \frac{ 11 }{ 5 } \right)^2}{ \frac{ 1 }{ 5 } } = 1 $$ | 2 |
221 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 36 } + \dfrac{ \left( y + 9 \right)^2}{ 49 } = 1 $$ | 2 |
222 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 25 } + \dfrac{ \left( y - 3 \right)^2}{ 36 } = 1 $$ | 2 |
223 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y + 3 \right)^2}{ 49 } = 1 $$ | 2 |
224 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 36 } = 1 $$ | 2 |
225 | 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 |
226 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 25 } = 1 $$ | 2 |
227 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 15129 }{ 4 } } + \dfrac{ y^2}{ \frac{ 15876 }{ 25 } } = 1 $$ | 2 |
228 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 899 }{ 100 } \right)^2}{ \frac{ 19 }{ 100 } } + \dfrac{ \left( y - \frac{ 53 }{ 20 } \right)^2}{ \frac{ 49 }{ 100 } } = 1 $$ | 2 |
229 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + 9y^2 = 36 $$ | 2 |
230 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 1 }{ 11 } } + \dfrac{ y^2}{ \frac{ 1 }{ 14 } } = 1 $$ | 2 |
231 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y + 4 \right)^2}{ 25 } = 1 $$ | 2 |
232 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 49 } + \dfrac{ \left( y + 3 \right)^2}{ 64 } = 1 $$ | 2 |
233 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 25 } + \dfrac{ \left( y + 4 \right)^2}{ 9 } = 1 $$ | 2 |
234 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 2 |
235 | 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 |
236 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 60 } = 1 $$ | 2 |
237 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 100 } + \dfrac{ y^2}{ \frac{ 9471 }{ 100 } } = 1 $$ | 2 |
238 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 25 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 2 |
239 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 64 } + \dfrac{ \left( y - 9 \right)^2}{ 49 } = 1 $$ | 2 |
240 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ \left( y + 1 \right)^2}{ 5 } = 1 $$ | 2 |
241 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 36 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 1 |
242 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 406 }{ 125 } } + \dfrac{ y^2}{ \frac{ 463 }{ 200 } } = 1 $$ | 1 |
243 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 16 \left( x - 2 \right)^2}{ 1 } + \dfrac{ 9 \left( y + 3 \right)^2}{ 1 } = 1 $$ | 1 |
244 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 49 } + \dfrac{ \left( y + 8 \right)^2}{ 64 } = 1 $$ | 1 |
245 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 36 } = 1 $$ | 1 |
246 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y + 5 \right)^2}{ 9 } = 1 $$ | 1 |
247 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 1 |
248 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 36 } + \dfrac{ \left( y + 1 \right)^2}{ 1 } = 1 $$ | 1 |
249 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 25 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 1 |
250 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 1 } + \dfrac{ 4 \left( y - 2 \right)^2}{ 1 } = 1 $$ | 1 |