Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 1101 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 144 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 1102 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 1103 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 18 \right)^2}{ 1 } + \dfrac{ \left( y - 14 \right)^2}{ 11 } = 1 $$ | 1 |
| 1104 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 1 } + \dfrac{ \left( y - 15 \right)^2}{ 11 } = 1 $$ | 1 |
| 1105 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 11 \right)^2}{ 122 } + \dfrac{ y^2}{ 131 } = 1 $$ | 1 |
| 1106 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 15 \right)^2}{ \frac{ 11089 }{ 250 } } + \dfrac{ \left( y - 13 \right)^2}{ \frac{ 109621 }{ 1000 } } = 1 $$ | 1 |
| 1107 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 1 |
| 1108 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y + 2 \right)^2}{ 49 } = 1 $$ | 1 |
| 1109 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 15 } + \dfrac{ \left( y - 8 \right)^2}{ 10 } = 1 $$ | 1 |
| 1110 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 10 } + \dfrac{ \left( y - 8 \right)^2}{ 15 } = 1 $$ | 1 |
| 1111 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 32 } + \dfrac{ y^2}{ 36 } = 1 $$ | 1 |
| 1112 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \sqrt{ 7 } } + \dfrac{ y^2}{ \sqrt{ 6 } } = 1 $$ | 1 |
| 1113 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 6x^2 + 2y^2 = 1 $$ | 1 |
| 1114 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 1 |
| 1115 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 1 |
| 1116 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ \frac{ 1 }{ 2 } } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 1 |
| 1117 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 7 \right)^2}{ 5.6169 } + \dfrac{ \left( y - \frac{ 27 }{ 100 } \right)^2}{ \frac{ 961 }{ 100 } } = 1 $$ | 1 |
| 1118 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 11 }{ 10 } } + \dfrac{ \left( y + \frac{ 13 }{ 2 } \right)^2}{ \frac{ 7 }{ 2 } } = 1 $$ | 1 |
| 1119 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ \left( y + \frac{ 13 }{ 2 } \right)^2}{ 2 } = 1 $$ | 1 |
| 1120 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 40 } = 1 $$ | 1 |
| 1121 | 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 |
| 1122 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 9 } = 1 $$ | 1 |
| 1123 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 9 \left( x - 1 \right)^2}{ 1 } + \dfrac{ 25 \left( y + 2 \right)^2}{ 1 } = 1 $$ | 1 |
| 1124 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 18 }{ 5 } } + \dfrac{ y^2}{ \frac{ 9 }{ 2 } } = 1 $$ | 1 |
| 1125 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 5 } + \dfrac{ \left( y + 1 \right)^2}{ 3 } = 1 $$ | 1 |
| 1126 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1618 } + \dfrac{ y^2}{ 1000 } = 1 $$ | 1 |
| 1127 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 36 } + \dfrac{ \left( y - 4 \right)^2}{ 34 } = 1 $$ | 1 |
| 1128 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 36 } + \dfrac{ \left( y - 4 \right)^2}{ 32 } = 1 $$ | 1 |
| 1129 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 1 |
| 1130 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 20 \right)^2}{ 225 } + \dfrac{ \left( y - 20 \right)^2}{ 400 } = 1 $$ | 1 |
| 1131 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 9 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 1 |
| 1132 | 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 |
| 1133 | 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 |
| 1134 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 7 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 1135 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 26 }{ 5 } \right)^2}{ \frac{ 1 }{ 200 } } + \dfrac{ \left( y - \frac{ 13 }{ 10 } \right)^2}{ \frac{ 1 }{ 10 } } = 1 $$ | 1 |
| 1136 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 1137 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 15 \right)^2}{ 2 } + \dfrac{ \left( y - 2 \right)^2}{ 2 } = 1 $$ | 1 |
| 1138 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 15 \right)^2}{ 2 } + \dfrac{ \left( y + 2 \right)^2}{ 2 } = 1 $$ | 1 |
| 1139 | 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 |
| 1140 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 4 \left( x + 3 \right)^2}{ 7 } + \dfrac{ 9 \left( y - 2 \right)^2}{ 11 } = 1 $$ | 1 |
| 1141 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 18 } + \dfrac{ y^2}{ 6 } = 1 $$ | 1 |
| 1142 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 1 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 1143 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 64 } + \dfrac{ \left( y + 4 \right)^2}{ 100 } = 1 $$ | 1 |
| 1144 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 1 |
| 1145 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 5 } = 1 $$ | 1 |
| 1146 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 9 \right)^2}{ 121 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 1147 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 81 } + \dfrac{ \left( y + 5 \right)^2}{ 16 } = 1 $$ | 1 |
| 1148 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 16x^2 + 9y^2 = 144 $$ | 1 |
| 1149 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 4y^2 = 4 $$ | 1 |
| 1150 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 15x^2 + 7y^2 = 105 $$ | 1 |
