Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 701 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 16 } = 1 $$ | 1 |
| 702 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + y^2 = 1 $$ | 1 |
| 703 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 12 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 704 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 26 } = 1 $$ | 1 |
| 705 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ 3 y^2}{ 1 } = 1 $$ | 1 |
| 706 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 16 } + \dfrac{ y^2}{ 7 } = 1 $$ | 1 |
| 707 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ y^2}{ 5 } = 1 $$ | 1 |
| 708 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 49 }{ 5 } } + \dfrac{ y^2}{ \frac{ 15 }{ 4 } } = 1 $$ | 1 |
| 709 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 710 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 23 } + \dfrac{ y^2}{ 36 } = 1 $$ | 1 |
| 711 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 80 } + \dfrac{ y^2}{ 49 } = 1 $$ | 1 |
| 712 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 11 } + \dfrac{ y^2}{ 49 } = 1 $$ | 1 |
| 713 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y + 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 714 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 8 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 715 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 9 \right)^2}{ 36 } + \dfrac{ \left( y - 6 \right)^2}{ 16 } = 1 $$ | 1 |
| 716 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 6 \right)^2}{ 9 } + \dfrac{ \left( y + 3 \right)^2}{ 16 } = 1 $$ | 1 |
| 717 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 6 \right)^2}{ 9 } + \dfrac{ \left( y + 3 \right)^2}{ 16 } = 1 $$ | 1 |
| 718 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 15 } + \dfrac{ y^2}{ 19 } = 1 $$ | 1 |
| 719 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 45 } + \dfrac{ \left( y - 1 \right)^2}{ 81 } = 1 $$ | 1 |
| 720 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
| 721 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 16 } + \dfrac{ \left( y - 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 722 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 1 |
| 723 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 55 } = 1 $$ | 1 |
| 724 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 8 } = 1 $$ | 1 |
| 725 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 15 } = 1 $$ | 1 |
| 726 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 47 } = 1 $$ | 1 |
| 727 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ \left( y - 5 \right)^2}{ 100 } = 1 $$ | 1 |
| 728 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 100 } + \dfrac{ \left( y - 10 \right)^2}{ 4 } = 1 $$ | 1 |
| 729 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 36 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 730 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 100 } + \dfrac{ \left( y - 6 \right)^2}{ 10 } = 1 $$ | 1 |
| 731 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 89 } + \dfrac{ \left( y - 7 \right)^2}{ 36 } = 1 $$ | 1 |
| 732 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 36 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 733 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 10 } + \dfrac{ y^2}{ 4 } = 1 $$ | 1 |
| 734 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 10 } + \dfrac{ \left( y - 4 \right)^2}{ 16 } = 1 $$ | 1 |
| 735 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 12 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 1 |
| 736 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 16 } = 1 $$ | 1 |
| 737 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 4 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 738 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 4 \left( x + 2 \right)^2}{ 1 } + \dfrac{ \left( y + 6 \right)^2}{ 4 } = 1 $$ | 1 |
| 739 | 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 |
| 740 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 10 } = 1 $$ | 1 |
| 741 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 137 } + \dfrac{ y^2}{ \frac{ 1507 }{ 10 } } = 1 $$ | 1 |
| 742 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 8 \right)^2}{ 64 } + \dfrac{ \left( y + 6 \right)^2}{ 49 } = 1 $$ | 1 |
| 743 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 25 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 1 |
| 744 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 1 |
| 745 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 746 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 19 }{ 10 } \right)^2}{ \frac{ 209 }{ 10 } } + \dfrac{ \left( y - 3 \right)^2}{ \frac{ 41 }{ 5 } } = 1 $$ | 1 |
| 747 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 9 }{ 10 } \right)^2}{ 18 } + \dfrac{ \left( y + \frac{ 31 }{ 10 } \right)^2}{ \frac{ 37 }{ 10 } } = 1 $$ | 1 |
| 748 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 71 }{ 10 } \right)^2}{ \frac{ 3 }{ 2 } } + \dfrac{ \left( y - \frac{ 49 }{ 5 } \right)^2}{ \frac{ 3 }{ 10 } } = 1 $$ | 1 |
| 749 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 24 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 750 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \sqrt{ 60 } } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
