Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 1001 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 4y^2 = 4 $$ | 1 |
| 1002 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 2y^2 = 6 $$ | 1 |
| 1003 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + y^2 = 27 $$ | 1 |
| 1004 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 3 } = 1 $$ | 1 |
| 1005 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 7 } = 1 $$ | 1 |
| 1006 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 12 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 1007 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 10y^2 = 50 $$ | 1 |
| 1008 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + y^2 = 27 $$ | 1 |
| 1009 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 15x^2 + 7y^2 = 105 $$ | 1 |
| 1010 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 4y^2 = 4 $$ | 1 |
| 1011 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 1012 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 1013 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 25 x^2}{ 9 } + \dfrac{ 9 \left( y - 12 \right)^2}{ 25 } = 1 $$ | 1 |
| 1014 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 75 } + \dfrac{ y^2}{ 50 } = 1 $$ | 1 |
| 1015 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 5 } + \dfrac{ y^2}{ 24 } = 1 $$ | 1 |
| 1016 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 50000 } + \dfrac{ y^2}{ 300000 } = 1 $$ | 1 |
| 1017 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 50000 } + \dfrac{ y^2}{ 30000 } = 1 $$ | 1 |
| 1018 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 3x^2 + 6y^2 = 1 $$ | 1 |
| 1019 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 25 } + \dfrac{ \left( y + 4 \right)^2}{ 4 } = 1 $$ | 1 |
| 1020 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 1021 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 1 } + \dfrac{ \left( y + 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 1022 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 25 } + \dfrac{ y^2}{ 4 } = 1 $$ | 1 |
| 1023 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 11 }{ 2 } } + \dfrac{ y^2}{ \frac{ 33 }{ 10 } } = 1 $$ | 1 |
| 1024 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 49 } = 1 $$ | 1 |
| 1025 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 6.1009 } + \dfrac{ y^2}{ 12.1801 } = 1 $$ | 1 |
| 1026 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 6.1009 } + \dfrac{ y^2}{ 15.5236 } = 1 $$ | 1 |
| 1027 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 12 \right)^2}{ 500 } + \dfrac{ \left( y - 10 \right)^2}{ 500 } = 1 $$ | 1 |
| 1028 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 1 |
| 1029 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 16 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 1030 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 1 |
| 1031 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 25 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 1 |
| 1032 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 1 |
| 1033 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y + 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 1034 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 1 |
| 1035 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 25 } + \dfrac{ \left( y + 3 \right)^2}{ 4 } = 1 $$ | 1 |
| 1036 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 16 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 1 |
| 1037 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 25 } = 1 $$ | 1 |
| 1038 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 100 } = 1 $$ | 1 |
| 1039 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 20 } = 1 $$ | 1 |
| 1040 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 3 \left( x + 1 \right)^2}{ 10 } + \dfrac{ 12 \left( y + 13 \right)^2}{ 10 } = 1 $$ | 1 |
| 1041 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 27 }{ 2 } } + \dfrac{ y^2}{ \frac{ 15 }{ 2 } } = 1 $$ | 1 |
| 1042 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 1043 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ 10 } = 1 $$ | 1 |
| 1044 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 1 }{ 2 } } + \dfrac{ y^2}{ \frac{ 21 }{ 50 } } = 1 $$ | 1 |
| 1045 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y + 5 \right)^2}{ 4 } = 1 $$ | 1 |
| 1046 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y + 5 \right)^2}{ 4 } = 1 $$ | 1 |
| 1047 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y + 5 \right)^2}{ 16 } = 1 $$ | 1 |
| 1048 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 5x^2 + 3y^2 = 1 $$ | 1 |
| 1049 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
| 1050 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
