Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 801 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 6 \right)^2}{ 36 } + \dfrac{ \left( y + 6 \right)^2}{ 25 } = 1 $$ | 1 |
| 802 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 36 } + \dfrac{ \left( y - 4 \right)^2}{ 25 } = 1 $$ | 1 |
| 803 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 25 } + \dfrac{ \left( y - 4 \right)^2}{ 36 } = 1 $$ | 1 |
| 804 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 49 } + \dfrac{ \left( y + 1 \right)^2}{ 33 } = 1 $$ | 1 |
| 805 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 5 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 1 |
| 806 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 81 } + \dfrac{ \left( y + 4 \right)^2}{ 65 } = 1 $$ | 1 |
| 807 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 1 } + \dfrac{ \left( y - 3 \right)^2}{ 65 } = 1 $$ | 1 |
| 808 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 809 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 21 } + \dfrac{ \left( y + 12 \right)^2}{ 120 } = 1 $$ | 1 |
| 810 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 49x^2 + 7y^2 = 49 $$ | 1 |
| 811 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 3x^2 + 4y^2 = 24 $$ | 1 |
| 812 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 3x^2 + 4y^2 = 24 $$ | 1 |
| 813 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 1 }{ 2 } } + \dfrac{ y^2}{ \frac{ 3 }{ 2 } } = 1 $$ | 1 |
| 814 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 1 |
| 815 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 49 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 816 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 16x^2 + 121y^2 = 1936 $$ | 1 |
| 817 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 18 } + \dfrac{ \left( y + 1 \right)^2}{ 20 } = 1 $$ | 1 |
| 818 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 18 } + \dfrac{ \left( y - 1 \right)^2}{ 20 } = 1 $$ | 1 |
| 819 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 4 } + \dfrac{ \left( y - \frac{ 9 }{ 2 } \right)^2}{ 9 } = 1 $$ | 1 |
| 820 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 42 } + \dfrac{ y^2}{ 32 } = 1 $$ | 1 |
| 821 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 1 |
| 822 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 15 } = 1 $$ | 1 |
| 823 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 7 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 824 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 625 } + \dfrac{ y^2}{ 49 } = 1 $$ | 1 |
| 825 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 41 } = 1 $$ | 1 |
| 826 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 18 \right)^2}{ 400 } + \dfrac{ \left( y + 12 \right)^2}{ \frac{ 78751 }{ 200 } } = 1 $$ | 1 |
| 827 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 18 \right)^2}{ 400 } + \dfrac{ y^2}{ \frac{ 78751 }{ 200 } } = 1 $$ | 1 |
| 828 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 18 \right)^2}{ 1 } + \dfrac{ \left( y + 12 \right)^2}{ \frac{ 78751 }{ 200 } } = 1 $$ | 1 |
| 829 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 400 } + \dfrac{ \left( y + 12 \right)^2}{ \frac{ 78751 }{ 200 } } = 1 $$ | 1 |
| 830 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 18 \right)^2}{ 400 } + \dfrac{ \left( y + 12 \right)^2}{ 1 } = 1 $$ | 1 |
| 831 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 8y^2 = 72 $$ | 1 |
| 832 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ 2 \left( y - 3 \right)^2}{ 1 } = 1 $$ | 1 |
| 833 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 169 } + \dfrac{ \left( y + 1 \right)^2}{ 144 } = 1 $$ | 1 |
| 834 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ \left( y - 4 \right)^2}{ 81 } = 1 $$ | 1 |
| 835 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 11 \right)^2}{ 22 } + \dfrac{ \left( y - 17 \right)^2}{ 20 } = 1 $$ | 1 |
| 836 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 6 } + \dfrac{ y^2}{ 8 } = 1 $$ | 1 |
| 837 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 8 } = 1 $$ | 1 |
| 838 | 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 |
| 839 | 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 |
| 840 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 4 } = 1 $$ | 1 |
| 841 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 5 } + \dfrac{ \left( y + 2 \right)^2}{ 4 } = 1 $$ | 1 |
| 842 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ \frac{ 23 }{ 5 } } + \dfrac{ \left( y + 2 \right)^2}{ 5 } = 1 $$ | 1 |
| 843 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 12 } + \dfrac{ \left( y - 4 \right)^2}{ 36 } = 1 $$ | 1 |
| 844 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 9 } + \dfrac{ y^2}{ 3 } = 1 $$ | 1 |
| 845 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 1 |
| 846 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 847 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 64 } = 1 $$ | 1 |
| 848 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 144 } + \dfrac{ \left( y - 1 \right)^2}{ 121 } = 1 $$ | 1 |
| 849 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ 9 y^2}{ 9 } = 1 $$ | 1 |
| 850 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 2 } + \dfrac{ y^2}{ 4 } = 1 $$ | 1 |
