Ellipse

(the database of solved problems)

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

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ID	Problem	Count
1	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{30} + \frac{y ^{2}}{5} = 1$	135
2	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{9} + \frac{y ^{2}}{36} = 1$	134
3	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$	104
4	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{12} + \frac{y ^{2}}{26} = 1$	100
5	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 2 ) ^{2}}{2} + \frac{y ^{2}}{4} = 1$	87
6	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{2} + \frac{y ^{2}}{3} = 1$	86
7	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{64} + \frac{y ^{2}}{25} = 1$	53
8	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{34} + \frac{y ^{2}}{25} = 1$	44
9	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{16} + \frac{y ^{2}}{4} = 1$	32
10	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{16} + \frac{y ^{2}}{36} = 1$	31
11	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{16} + \frac{y ^{2}}{21} = 1$	29
12	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $9 x^{2} + 16 y^{2} = 144$	29
13	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$	28
14	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 4 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{25} = 1$	25
15	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x + 9 ) ^{2}}{16} + \frac{( y + 8 ) ^{2}}{25} = 1$	24
16	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{4} + \frac{y ^{2}}{25} = 1$	23
17	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 1$	22
18	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 9 ) ^{2}}{81} + \frac{( y - 4 ) ^{2}}{49} = 1$	22
19	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 3 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{100} = 1$	20
20	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $25 x^{2} + 9 y^{2} = 225$	18
21	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 18 ) ^{2}}{400} + \frac{( y + 12 ) ^{2}}{\frac{78751}{200}} = 1$	18
22	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1$	17
23	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x + 6 ) ^{2}}{100} + \frac{( y + 2 ) ^{2}}{15} = 1$	16
24	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x + 4 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{9} = 1$	16
25	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{3} + \frac{y ^{2}}{2} = 1$	14
26	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1$	14
27	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{25} + \frac{y ^{2}}{36} = 1$	12
28	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{49} + \frac{y ^{2}}{4} = 1$	10
29	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1$	10
30	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{4} = 1$	10
31	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{4} = 1$	10
32	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{14400} + \frac{y ^{2}}{4096} = 1$	9
33	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1$	9
34	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{25} + \frac{y ^{2}}{4} = 1$	9
35	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $4 x^{2} + 9 y^{2} = 36$	9
36	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $9 x^{2} + 25 y^{2} = 225$	8
37	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{4} + \frac{y ^{2}}{49} = 1$	8
38	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 5 ) ^{2}}{36} + \frac{( y - 9 ) ^{2}}{49} = 1$	8
39	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{225} + \frac{y ^{2}}{196} = 1$	8
40	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $x^{2} + 4 y^{2} = 1$	8
41	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 2 ) ^{2}}{64} + \frac{( y - 4 ) ^{2}}{16} = 1$	8
42	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{52} + \frac{y ^{2}}{36} = 1$	7
43	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{676} + \frac{y ^{2}}{576} = 1$	7
44	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{25} + \frac{y ^{2}}{36} = 1$	7
45	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{4} = 1$	7
46	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{49} + \frac{( y - 3 ) ^{2}}{9} = 1$	7
47	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x + 6 ) ^{2}}{49} + \frac{( y + 3 ) ^{2}}{64} = 1$	6
48	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1$	6
49	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{x ^{2}}{81} + \frac{y ^{2}}{16} = 1$	6
50	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse: $\frac{( x - 4 ) ^{2}}{\frac{1}{10}} + \frac{( y + 1 ) ^{2}}{5} = 1$	6