Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 651 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 9 } + \dfrac{ \left( y - 5 \right)^2}{ 1 } = 1 $$ | 1 |
| 652 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 653 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 5 } + \dfrac{ y^2}{ 10 } = 1 $$ | 1 |
| 654 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ \left( y + 5 \right)^2}{ 12 } = 1 $$ | 1 |
| 655 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 62 } + \dfrac{ y^2}{ 36 } = 1 $$ | 1 |
| 656 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 11 } = 1 $$ | 1 |
| 657 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 58 } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
| 658 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 3 } = 1 $$ | 1 |
| 659 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 18 } + \dfrac{ y^2}{ 22 } = 1 $$ | 1 |
| 660 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 81 } + \dfrac{ \left( y + 8 \right)^2}{ 25 } = 1 $$ | 1 |
| 661 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 81 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 662 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 64 } + \dfrac{ y^2}{ 49 } = 1 $$ | 1 |
| 663 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 6 \right)^2}{ 9 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 664 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 81 } + \dfrac{ \left( y - 1 \right)^2}{ 24 } = 1 $$ | 1 |
| 665 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 83 } + \dfrac{ \left( y + 6 \right)^2}{ 64 } = 1 $$ | 1 |
| 666 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 4y^2 = 1 $$ | 1 |
| 667 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 17434 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 668 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 1 }{ 2 } } + \dfrac{ y^2}{ 7 } = 1 $$ | 1 |
| 669 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 5 } = 1 $$ | 1 |
| 670 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 30 } + \dfrac{ y^2}{ 1 } = 1 $$ | 1 |
| 671 | 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 |
| 672 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 9 } + \dfrac{ y^2}{ 5 } = 1 $$ | 1 |
| 673 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 7 } + \dfrac{ y^2}{ 3 } = 1 $$ | 1 |
| 674 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 12 } = 1 $$ | 1 |
| 675 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 16 \left( x + 1 \right)^2}{ 400 } + \dfrac{ 25 \left( y + 36 \right)^2}{ 400 } = 1 $$ | 1 |
| 676 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 15 \left( x + 1 \right)^2}{ 400 } + \dfrac{ 25 \left( y + 6 \right)^2}{ 400 } = 1 $$ | 1 |
| 677 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 2 \left( x + 2 \right)^2}{ 32 } + \dfrac{ \left( y + 5 \right)^2}{ 32 } = 1 $$ | 1 |
| 678 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 49 } + \dfrac{ \left( y + 6 \right)^2}{ 100 } = 1 $$ | 1 |
| 679 | 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 |
| 680 | 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 |
| 681 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 1 |
| 682 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y + 3 \right)^2}{ 4 } = 1 $$ | 1 |
| 683 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 1 |
| 684 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 1 |
| 685 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 289 } + \dfrac{ y^2}{ 36 } = 1 $$ | 1 |
| 686 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 1 |
| 687 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 111 }{ 2 } } + \dfrac{ y^2}{ \frac{ 95 }{ 2 } } = 1 $$ | 1 |
| 688 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 45 } + \dfrac{ y^2}{ 81 } = 1 $$ | 1 |
| 689 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 81 } + \dfrac{ \left( y - 3 \right)^2}{ 32 } = 1 $$ | 1 |
| 690 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ \left( y + 4 \right)^2}{ 16 } = 1 $$ | 1 |
| 691 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + 9y^2 = 36 $$ | 1 |
| 692 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1940 } + \dfrac{ y^2}{ 440 } = 1 $$ | 1 |
| 693 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3800 } + \dfrac{ y^2}{ 900 } = 1 $$ | 1 |
| 694 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + 7y^2 = 8 $$ | 1 |
| 695 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 25 } + \dfrac{ \left( y - 5 \right)^2}{ 81 } = 1 $$ | 1 |
| 696 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 697 | 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 |
| 698 | 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 |
| 699 | 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 |
| 700 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 9y^2 = 36 $$ | 1 |
