Ellipse – Solved Problems Database
All the problems and solutions shown below were generated using the Ellipse Calculator.
ID |
Problem |
Count |
1 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 3 } = 1 $$ | 12 |
2 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 18 \right)^2}{ 400 } + \dfrac{ \left( y + 12 \right)^2}{ \frac{ 78751 }{ 200 } } = 1 $$ | 11 |
3 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 4 } = 1 $$ | 11 |
4 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 10 |
5 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 16y^2 = 144 $$ | 10 |
6 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 12 } + \dfrac{ y^2}{ 26 } = 1 $$ | 9 |
7 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 4 } = 1 $$ | 9 |
8 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 36 } = 1 $$ | 8 |
9 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 9 } = 1 $$ | 8 |
10 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 25 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 8 |
11 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 25 } = 1 $$ | 7 |
12 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 2 } + \dfrac{ y^2}{ 4 } = 1 $$ | 6 |
13 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 30 } + \dfrac{ y^2}{ 5 } = 1 $$ | 6 |
14 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 25 } = 1 $$ | 6 |
15 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 34 } + \dfrac{ y^2}{ 25 } = 1 $$ | 6 |
16 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$ | 6 |
17 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 16 } = 1 $$ | 6 |
18 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 36 } + \dfrac{ \left( y + 5 \right)^2}{ 100 } = 1 $$ | 6 |
19 | 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 |
20 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + 9y^2 = 225 $$ | 5 |
21 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 5 |
22 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 9 } = 1 $$ | 5 |
23 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 9 \right)^2}{ 16 } + \dfrac{ \left( y + 8 \right)^2}{ 25 } = 1 $$ | 5 |
24 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 25 } = 1 $$ | 5 |
25 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ \sqrt{ 21 } } = 1 $$ | 5 |
26 | 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 |
27 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ 2 } = 1 $$ | 4 |
28 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 14400 } + \dfrac{ y^2}{ 4096 } = 1 $$ | 4 |
29 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + y^2 = 81 $$ | 4 |
30 | 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 |
31 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 9 \right)^2}{ 81 } + \dfrac{ \left( y - 4 \right)^2}{ 49 } = 1 $$ | 4 |
32 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 36 } = 1 $$ | 4 |
33 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 3 |
34 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 3 |
35 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 18 \right)^2}{ \frac{ 393 }{ 100 } } + \dfrac{ \left( y + 12 \right)^2}{ 400 } = 1 $$ | 3 |
36 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 25 } = 1 $$ | 3 |
37 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 25 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 3 |
38 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 4 } + \dfrac{ \left( y + 5 \right)^2}{ 25 } = 1 $$ | 3 |
39 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 25 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 3 |
40 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 14 } + \dfrac{ y^2}{ 9 } = 1 $$ | 3 |
41 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 3 |
42 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 25 } + \dfrac{ \left( y - 4 \right)^2}{ 4 } = 1 $$ | 3 |
43 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 64 } + \dfrac{ \left( y + 4 \right)^2}{ 25 } = 1 $$ | 3 |
44 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 100 } + \dfrac{ \left( y + 2 \right)^2}{ 15 } = 1 $$ | 3 |
45 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 3 |
46 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 15 } + \dfrac{ y^2}{ 30 } = 1 $$ | 3 |
47 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 100 } + \dfrac{ \left( y - 6 \right)^2}{ 1 } = 1 $$ | 3 |
48 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 8 \right)^2}{ 25 } + \dfrac{ \left( y + 9 \right)^2}{ 16 } = 1 $$ | 3 |
49 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 4 } + \dfrac{ \left( y + 1 \right)^2}{ 9 } = 1 $$ | 3 |
50 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 36 } + \dfrac{ \left( y - 3 \right)^2}{ 9 } = 1 $$ | 3 |