Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 101 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 5 |
| 102 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 144 } + \dfrac{ \left( y - 1 \right)^2}{ 121 } = 1 $$ | 5 |
| 103 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 81 } + \dfrac{ y^2}{ 49 } = 1 $$ | 5 |
| 104 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 9 \left( x + 1 \right)^2}{ 1 } + \dfrac{ \left( y + 8 \right)^2}{ 8 } = 1 $$ | 5 |
| 105 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 9 } + \dfrac{ \left( y + 5 \right)^2}{ 4 } = 1 $$ | 5 |
| 106 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 100 } = 1 $$ | 5 |
| 107 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 100 } + \dfrac{ \left( y + 5 \right)^2}{ 64 } = 1 $$ | 5 |
| 108 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 9 } + \dfrac{ \left( y + 29 \right)^2}{ 16 } = 1 $$ | 5 |
| 109 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 81 } = 1 $$ | 5 |
| 110 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 25 } = 1 $$ | 5 |
| 111 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ 4 } = 1 $$ | 5 |
| 112 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 1 } = 1 $$ | 5 |
| 113 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + 16y^2 = 400 $$ | 5 |
| 114 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 16 } = 1 $$ | 5 |
| 115 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 8 \right)^2}{ 4 } + \dfrac{ \left( y + 10 \right)^2}{ 25 } = 1 $$ | 5 |
| 116 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 81 } + \dfrac{ 4 \left( y - 3 \right)^2}{ 25 } = 1 $$ | 5 |
| 117 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 2 } + \dfrac{ \left( y - 1 \right)^2}{ 1 } = 1 $$ | 5 |
| 118 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 16 } = 1 $$ | 5 |
| 119 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + 94y^2 = 100 $$ | 5 |
| 120 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 5 |
| 121 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 4 } = 1 $$ | 5 |
| 122 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 100 } = 1 $$ | 5 |
| 123 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ \left( y - 3 \right)^2}{ 25 } = 1 $$ | 5 |
| 124 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 1 } + \dfrac{ \left( y + 2 \right)^2}{ 5 } = 1 $$ | 5 |
| 125 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 1 } = 1 $$ | 5 |
| 126 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 71 }{ 10 } } + \dfrac{ y^2}{ 7 } = 1 $$ | 5 |
| 127 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 4 \left( x - 3 \right)^2}{ 12 } + \dfrac{ 8 \left( y + 6 \right)^2}{ 20 } = 1 $$ | 5 |
| 128 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 10 } + \dfrac{ y^2}{ 20 } = 1 $$ | 5 |
| 129 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 36 } + \dfrac{ \left( y + 6 \right)^2}{ 196 } = 1 $$ | 5 |
| 130 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 12 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 5 |
| 131 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 81 } + \dfrac{ y^2}{ 25 } = 1 $$ | 5 |
| 132 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 41 } + \dfrac{ y^2}{ 25 } = 1 $$ | 5 |
| 133 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ \frac{ 3 }{ 2 } } = 1 $$ | 4 |
| 134 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 4 |
| 135 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 0.9165y^2 = 1 $$ | 4 |
| 136 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y + 2 \right)^2}{ 9 } = 1 $$ | 4 |
| 137 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 15 } + \dfrac{ y^2}{ 5 } = 1 $$ | 4 |
| 138 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 25 } + \dfrac{ y^2}{ 16 } = 1 $$ | 4 |
| 139 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 91 \left( x + 1 \right)^2}{ 1 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$ | 4 |
| 140 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 1 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$ | 4 |
| 141 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y + 4 \right)^2}{ 4 } = 1 $$ | 4 |
| 142 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 9 } + \dfrac{ \left( y - 8 \right)^2}{ 25 } = 1 $$ | 4 |
| 143 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 5 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 4 |
| 144 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 10 \right)^2}{ 175 } + \dfrac{ \left( y + 2 \right)^2}{ 15 } = 1 $$ | 4 |
| 145 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 36 \left( x + 1 \right)^2}{ 1 } + \dfrac{ \left( y - 8 \right)^2}{ 2 } = 1 $$ | 4 |
| 146 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 25 } = 1 $$ | 4 |
| 147 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 25 } + \dfrac{ \left( y - 5 \right)^2}{ 16 } = 1 $$ | 4 |
| 148 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 4 } = 1 $$ | 4 |
| 149 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \sqrt{ 2 } } + \dfrac{ y^2}{ 1 } = 1 $$ | 4 |
| 150 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 25 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 4 |
