Ellipse – Solved Problems Database
All the problems and solutions shown below were generated using the Ellipse Calculator.
ID |
Problem |
Count |
51 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 10 \right)^2}{ 81 } + \dfrac{ \left( y - 1 \right)^2}{ 1 } = 1 $$ | 3 |
52 | 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 |
53 | 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 |
54 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 16x^2 + 49y^2 = 784 $$ | 3 |
55 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y - 3 \right)^2}{ 36 } = 1 $$ | 3 |
56 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 7 \right)^2}{ 9 } + \dfrac{ \left( y + 3 \right)^2}{ 49 } = 1 $$ | 3 |
57 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 7 }{ 2 } \right)^2}{ \frac{ 11 }{ 2 } } + \dfrac{ \left( y - 1 \right)^2}{ 3 } = 1 $$ | 3 |
58 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 9 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 1 \right)^2}{ 5 } = 1 $$ | 3 |
59 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 11 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 1 \right)^2}{ 5 } = 1 $$ | 3 |
60 | 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 |
61 | 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 |
62 | 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 |
63 | 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 |
64 | 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 |
65 | 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 |
66 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 4 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 3 |
67 | 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 |
68 | 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 |
69 | 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 |
70 | 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 |
71 | 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 |
72 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 11 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y - 1 \right)^2}{ 5 } = 1 $$ | 3 |
73 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 1 } = 1 $$ | 3 |
74 | 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 |
75 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 8 \right)^2}{ 25 } + \dfrac{ \left( y - 7 \right)^2}{ 49 } = 1 $$ | 3 |
76 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y - 1 \right)^2}{ 5 } = 1 $$ | 3 |
77 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 6 } + \dfrac{ \left( y - 2 \right)^2}{ 49 } = 1 $$ | 3 |
78 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 7 }{ 2 } \right)^2}{ 4 } + \dfrac{ \left( y + \frac{ 5 }{ 2 } \right)^2}{ 2 } = 1 $$ | 3 |
79 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 1 \right)^2}{ 5 } = 1 $$ | 3 |
80 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 16 } = 1 $$ | 3 |
81 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 49 } = 1 $$ | 3 |
82 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 436 } = 1 $$ | 3 |
83 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 25 } + \dfrac{ \left( y + 4 \right)^2}{ 9 } = 1 $$ | 3 |
84 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 7 } + \dfrac{ \left( y + 6 \right)^2}{ 1 } = 1 $$ | 3 |
85 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - \frac{ 293 }{ 25 } \right)^2}{ \frac{ 1 }{ 4 } } + \dfrac{ \left( y - \frac{ 131 }{ 50 } \right)^2}{ \frac{ 9 }{ 20 } } = 1 $$ | 2 |
86 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 1 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 2 |
87 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 16 } = 1 $$ | 2 |
88 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 25 } + \dfrac{ \left( y - 1 \right)^2}{ 4 } = 1 $$ | 2 |
89 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 9 \right)^2}{ 16 } + \dfrac{ \left( y + 9 \right)^2}{ 25 } = 1 $$ | 2 |
90 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 21 }{ 2 } \right)^2}{ 1 } + \dfrac{ \left( y + 1 \right)^2}{ \frac{ 1 }{ 100 } } = 1 $$ | 2 |
91 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 3 \left( x - 3 \right)^2}{ 1 } + \dfrac{ \frac{ 4 }{ 3 } \left( y + 5 \right)^2}{ 1 } = 1 $$ | 2 |
92 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 2 \left( x + 2 \right)^2}{ 2 } + \dfrac{ 2 \left( y + 2 \right)^2}{ 2 } = 1 $$ | 2 |
93 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 4 } + \dfrac{ \left( y + 1 \right)^2}{ 64 } = 1 $$ | 2 |
94 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 4 } = 1 $$ | 2 |
95 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 64 } + \dfrac{ \left( y + 4 \right)^2}{ 9 } = 1 $$ | 2 |
96 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ \frac{ 136 }{ 25 } } + \dfrac{ \left( y - 5 \right)^2}{ 34 } = 1 $$ | 2 |
97 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 5 } + \dfrac{ \left( y + \frac{ 3 }{ 2 } \right)^2}{ \frac{ 3 }{ 2 } } = 1 $$ | 2 |
98 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 16 x^2}{ 1 } + \dfrac{ y^2}{ 1 } = 1 $$ | 2 |
99 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 9 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 2 |
100 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 10 \right)^2}{ 121 } + \dfrac{ \left( y + 3 \right)^2}{ 49 } = 1 $$ | 2 |