Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 751 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 12 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 1 |
| 752 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 1 } + \dfrac{ \left( y - 4 \right)^2}{ \frac{ 1 }{ 4 } } = 1 $$ | 1 |
| 753 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 1 } + \dfrac{ \left( y + 4 \right)^2}{ \frac{ 1 }{ 4 } } = 1 $$ | 1 |
| 754 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 9y^2 = 36 $$ | 1 |
| 755 | 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 |
| 756 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + y^2 = 1 $$ | 1 |
| 757 | 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 |
| 758 | 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 |
| 759 | 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 |
| 760 | 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 |
| 761 | 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 |
| 762 | 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 |
| 763 | 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 |
| 764 | 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 |
| 765 | 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 |
| 766 | 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 |
| 767 | 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 |
| 768 | 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 |
| 769 | 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 |
| 770 | 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 |
| 771 | 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 |
| 772 | 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 |
| 773 | 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 |
| 774 | 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 |
| 775 | 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 |
| 776 | 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 |
| 777 | 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 |
| 778 | 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 |
| 779 | 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 |
| 780 | 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 |
| 781 | 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 |
| 782 | 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 |
| 783 | 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 |
| 784 | 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 |
| 785 | 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 |
| 786 | 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 |
| 787 | 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 |
| 788 | 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 |
| 789 | 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 |
| 790 | 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 |
| 791 | 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 |
| 792 | 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 |
| 793 | 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 |
| 794 | 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 |
| 795 | 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 |
| 796 | 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 |
| 797 | 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 |
| 798 | 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 |
| 799 | 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 |
| 800 | 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 |
