Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 1051 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 64 } + \dfrac{ \left( y + 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1052 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 81 } + \dfrac{ \left( y - 1 \right)^2}{ 144 } = 1 $$ | 1 |
| 1053 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 2y^2 = 1 $$ | 1 |
| 1054 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y - 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1055 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 25 } + \dfrac{ \left( y + 3 \right)^2}{ 36 } = 1 $$ | 1 |
| 1056 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 1 } + \dfrac{ \left( y + 3 \right)^2}{ 25 } = 1 $$ | 1 |
| 1057 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 8 \right)^2}{ 1 } + \dfrac{ \left( y + 2 \right)^2}{ 49 } = 1 $$ | 1 |
| 1058 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 4 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 1059 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1.5384 } + \dfrac{ y^2}{ 0.5541 } = 1 $$ | 1 |
| 1060 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1.6143 } + \dfrac{ y^2}{ 0.4317 } = 1 $$ | 1 |
| 1061 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 0.2697 } + \dfrac{ y^2}{ \frac{ 51 }{ 250 } } = 1 $$ | 1 |
| 1062 | 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 |
| 1063 | 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 |
| 1064 | 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 |
| 1065 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 9 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 13 } = 1 $$ | 1 |
| 1066 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 1 } + \dfrac{ \left( y + 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1067 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 28 } + \dfrac{ y^2}{ 22 } = 1 $$ | 1 |
| 1068 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 81 }{ 4 } } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 1069 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 9 } + \dfrac{ \left( y - 5 \right)^2}{ 45 } = 1 $$ | 1 |
| 1070 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 9 } + \dfrac{ \left( y - 5 \right)^2}{ 36 } = 1 $$ | 1 |
| 1071 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 36 } + \dfrac{ \left( y - 5 \right)^2}{ 9 } = 1 $$ | 1 |
| 1072 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 45 } + \dfrac{ \left( y - 5 \right)^2}{ 9 } = 1 $$ | 1 |
| 1073 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y - 3 \right)^2}{ 49 } = 1 $$ | 1 |
| 1074 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 144 } + \dfrac{ y^2}{ 196 } = 1 $$ | 1 |
| 1075 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 16 } + \dfrac{ \left( y + 5 \right)^2}{ 25 } = 1 $$ | 1 |
| 1076 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 64 } = 1 $$ | 1 |
| 1077 | 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 |
| 1078 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 12x^2 + 3y^2 = 48 $$ | 1 |
| 1079 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 4 }{ 3 } } + \dfrac{ y^2}{ \frac{ 3 }{ 2 } } = 1 $$ | 1 |
| 1080 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 9 }{ 8 } } + \dfrac{ y^2}{ \frac{ 16 }{ 9 } } = 1 $$ | 1 |
| 1081 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \frac{ 4 }{ 3 }x^2 + \frac{ 3 }{ 2 }y^2 = 2 $$ | 1 |
| 1082 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 21 } + \dfrac{ \left( y - 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1083 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 16x^2 + 64y^2 = 4096 $$ | 1 |
| 1084 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 1085 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 36 } + \dfrac{ \left( y - 1 \right)^2}{ 16 } = 1 $$ | 1 |
| 1086 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 4 } = 1 $$ | 1 |
| 1087 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 25 } + \dfrac{ \left( y + 3 \right)^2}{ 4 } = 1 $$ | 1 |
| 1088 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 16 } + \dfrac{ \left( y - 4 \right)^2}{ 8 } = 1 $$ | 1 |
| 1089 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 9 } + \dfrac{ \left( y - 5 \right)^2}{ 9 } = 1 $$ | 1 |
| 1090 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 1 |
| 1091 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + 4y^2 = 11 $$ | 1 |
| 1092 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 1 } = 1 $$ | 1 |
| 1093 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y - 1 \right)^2}{ 1 } = 1 $$ | 1 |
| 1094 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 1 } = 1 $$ | 1 |
| 1095 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 1 } = 1 $$ | 1 |
| 1096 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 5 } + \dfrac{ \left( y - 3 \right)^2}{ 4 } = 1 $$ | 1 |
| 1097 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 1 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 1098 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 81 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 1099 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 1100 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 16 } + \dfrac{ \left( y - 3 \right)^2}{ 4 } = 1 $$ | 1 |
