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:$$ \dfrac{ x^2}{ 64 } + \dfrac{ y^2}{ 25 } = 1 $$	380
2	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 2 } + \dfrac{ y^2}{ 4 } = 1 $$	280
3	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 9 } = 1 $$	265
4	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 12 } + \dfrac{ y^2}{ 26 } = 1 $$	261
5	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 36 } = 1 $$	241
6	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 30 } + \dfrac{ y^2}{ 5 } = 1 $$	221
7	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 3 } = 1 $$	140
8	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 9 \right)^2}{ 16 } + \dfrac{ \left( y + 8 \right)^2}{ 25 } = 1 $$	118
9	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 36 } + \dfrac{ \left( y + 5 \right)^2}{ 100 } = 1 $$	113
10	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 18 \right)^2}{ 400 } + \dfrac{ \left( y + 12 \right)^2}{ \frac{ 78751 }{ 200 } } = 1 $$	109
11	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 16y^2 = 144 $$	104
12	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 4 } = 1 $$	93
13	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 34 } + \dfrac{ y^2}{ 25 } = 1 $$	77
14	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 4 } = 1 $$	73
15	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$	65
16	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 25 } = 1 $$	54
17	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 36 } = 1 $$	49
18	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 4 } = 1 $$	46
19	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 16 } = 1 $$	43
20	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ \sqrt{ 21 } } = 1 $$	43
21	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 9 } = 1 $$	39
22	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$	36
23	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 25x^2 + 9y^2 = 225 $$	33
24	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 9 \right)^2}{ 81 } + \dfrac{ \left( y - 4 \right)^2}{ 49 } = 1 $$	29
25	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 16 } = 1 $$	29
26	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 100 } + \dfrac{ \left( y + 2 \right)^2}{ 15 } = 1 $$	22
27	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 25 } = 1 $$	19
28	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 22500 } + \dfrac{ y^2}{ 21600 } = 1 $$	19
29	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ 2 } = 1 $$	19
30	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 9 } = 1 $$	18
31	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
32	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 64 } + \dfrac{ \left( y - 4 \right)^2}{ 16 } = 1 $$	16
33	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 676 } + \dfrac{ y^2}{ 576 } = 1 $$	16
34	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 36 } + \dfrac{ \left( y - 9 \right)^2}{ 49 } = 1 $$	14
35	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 49 } = 1 $$	13
36	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
37	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
38	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 4 } = 1 $$	12
39	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 49 } + \dfrac{ \left( y + 3 \right)^2}{ 64 } = 1 $$	11
40	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
41	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + 9y^2 = 36 $$	10
42	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 144 } + \dfrac{ y^2}{ 169 } = 1 $$	10
43	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 30625 } + \dfrac{ y^2}{ 2500 } = 1 $$	10
44	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
45	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
46	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 20 } + \dfrac{ y^2}{ 36 } = 1 $$	9
47	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
48	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 2 } = 1 $$	9
49	Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 16 } = 1 $$	9
50	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