Ellipse

(the database of solved problems)

All the problems and solutions shown below were generated using the Ellipse Calculator.

Select category

ID	Problem	Count
1	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 12 } + \dfrac{ y^2}{ 26 } = 1 $$	204
2	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 36 } = 1 $$	191
3	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 30 } + \dfrac{ y^2}{ 5 } = 1 $$	188
4	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 25 } = 1 $$	160
5	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 2 } + \dfrac{ y^2}{ 4 } = 1 $$	154
6	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 9 } = 1 $$	152
7	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 3 } = 1 $$	129
8	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 16y^2 = 144 $$	71
9	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 4 } = 1 $$	68
10	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 9 \right)^2}{ 16 } + \dfrac{ \left( y + 8 \right)^2}{ 25 } = 1 $$	63
11	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 34 } + \dfrac{ y^2}{ 25 } = 1 $$	60
12	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 36 } + \dfrac{ \left( y + 5 \right)^2}{ 100 } = 1 $$	59
13	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 18 \right)^2}{ 400 } + \dfrac{ \left( y + 12 \right)^2}{ \frac{ 78751 }{ 200 } } = 1 $$	41
14	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 36 } = 1 $$	36
15	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 4 } = 1 $$	35
16	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 4 } = 1 $$	34
17	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ \sqrt{ 21 } } = 1 $$	32
18	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 16 } = 1 $$	32
19	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$	32
20	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$	28
21	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 25 } = 1 $$	27
22	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 9 \right)^2}{ 81 } + \dfrac{ \left( y - 4 \right)^2}{ 49 } = 1 $$	24
23	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 9 } = 1 $$	22
24	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + 9y^2 = 225 $$	20
25	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 100 } + \dfrac{ \left( y + 2 \right)^2}{ 15 } = 1 $$	19
26	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ 2 } = 1 $$	16
27	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$	16
28	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 676 } + \dfrac{ y^2}{ 576 } = 1 $$	13
29	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 36 } = 1 $$	12
30	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 4 } = 1 $$	12
31	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 25 } = 1 $$	12
32	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + 9y^2 = 36 $$	10
33	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 16 } = 1 $$	10
34	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 25 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$	10
35	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 36 } + \dfrac{ \left( y - 9 \right)^2}{ 49 } = 1 $$	10
36	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 25 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$	10
37	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 16 } = 1 $$	9
38	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 4 } = 1 $$	9
39	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 64 } + \dfrac{ \left( y - 4 \right)^2}{ 16 } = 1 $$	9
40	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 14400 } + \dfrac{ y^2}{ 4096 } = 1 $$	9
41	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 225 } + \dfrac{ y^2}{ 196 } = 1 $$	8
42	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 4 } + \dfrac{ \left( y + 2 \right)^2}{ 16 } = 1 $$	8
43	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 2 } = 1 $$	8
44	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 9 } = 1 $$	8
45	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 25y^2 = 225 $$	8
46	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 4y^2 = 1 $$	8
47	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 49 } = 1 $$	8
48	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 49 } + \dfrac{ \left( y + 3 \right)^2}{ 64 } = 1 $$	7
49	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 436 } = 1 $$	7
50	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 52 } + \dfrac{ y^2}{ 36 } = 1 $$	7