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:$$ \dfrac{ \left( x - 1 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 1102 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 14 } = 1 $$ | 1 |
| 1103 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 64 } + \dfrac{ y^2}{ 81 } = 1 $$ | 1 |
| 1104 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 81 } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
| 1105 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 16 } = 1 $$ | 1 |
| 1106 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1107 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 1 |
| 1108 | 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 |
| 1109 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 25 } + \dfrac{ \left( y + 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 1110 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 8 \right)^2}{ 1 } + \dfrac{ \left( y - 3 \right)^2}{ 49 } = 1 $$ | 1 |
| 1111 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 7 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 1112 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 25 \right)^2}{ 16 } + \dfrac{ \left( y - 9 \right)^2}{ 9 } = 1 $$ | 1 |
| 1113 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 25 \right)^2}{ 1 } + \dfrac{ \left( y - 9 \right)^2}{ 9 } = 1 $$ | 1 |
| 1114 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y - 3 \right)^2}{ 1 } = 1 $$ | 1 |
| 1115 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 54 } + \dfrac{ y^2}{ 36 } = 1 $$ | 1 |
| 1116 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 10 } = 1 $$ | 1 |
| 1117 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 30 } = 1 $$ | 1 |
| 1118 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 91 } + \dfrac{ y^2}{ 100 } = 1 $$ | 1 |
| 1119 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 20 } + \dfrac{ y^2}{ 69 } = 1 $$ | 1 |
| 1120 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 10 \right)^2}{ 81 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 1121 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 10 \right)^2}{ 25 } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
| 1122 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 4 \left( x + 1 \right)^2}{ \frac{ 3 }{ 2 } } + \dfrac{ \left( y - 2 \right)^2}{ 3 } = 1 $$ | 1 |
| 1123 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 9 } + \dfrac{ \left( y - 5 \right)^2}{ 64 } = 1 $$ | 1 |
| 1124 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 32 } + \dfrac{ y^2}{ 40 } = 1 $$ | 1 |
| 1125 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 32 } + \dfrac{ y^2}{ 34 } = 1 $$ | 1 |
| 1126 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 58 } + \dfrac{ y^2}{ 228 } = 1 $$ | 1 |
| 1127 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 327 } + \dfrac{ y^2}{ 160 } = 1 $$ | 1 |
| 1128 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 1 } = 1 $$ | 1 |
| 1129 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 7 } + \dfrac{ \left( y + 2 \right)^2}{ 3 } = 1 $$ | 1 |
| 1130 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 36 } + \dfrac{ \left( y + 6 \right)^2}{ 4 } = 1 $$ | 1 |
| 1131 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1132 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 18 } + \dfrac{ y^2}{ \frac{ 12 }{ 5 } } = 1 $$ | 1 |
| 1133 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 5 } + \dfrac{ y^2}{ 2 } = 1 $$ | 1 |
| 1134 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 1 } = 1 $$ | 1 |
| 1135 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 144x^2 + y^2 = 144 $$ | 1 |
| 1136 | 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 |
| 1137 | 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 |
| 1138 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 2y^2 = 1 $$ | 1 |
| 1139 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y - 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 1140 | 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 |
| 1141 | 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 |
| 1142 | 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 |
| 1143 | 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 |
| 1144 | 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 |
| 1145 | 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 |
| 1146 | 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 |
| 1147 | 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 |
| 1148 | 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 |
| 1149 | 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 |
| 1150 | 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 |
