Ellipse – Solved Problems Database
All the problems and solutions shown below were generated using the Ellipse Calculator.
ID |
Problem |
Count |
101 | 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 |
102 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 4 } = 1 $$ | 2 |
103 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 4 } = 1 $$ | 2 |
104 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$ | 2 |
105 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 36 } + \dfrac{ 4 \left( y + 6 \right)^2}{ 9 } = 1 $$ | 2 |
106 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 2 |
107 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 7 \right)^2}{ 25 } + \dfrac{ \left( y - 25 \right)^2}{ 16 } = 1 $$ | 2 |
108 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 36 } + \dfrac{ \left( y + 3 \right)^2}{ 4 } = 1 $$ | 2 |
109 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 9 } = 1 $$ | 2 |
110 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 16 } = 1 $$ | 2 |
111 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 16 } = 1 $$ | 2 |
112 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 4 \left( x - 4 \right)^2}{ 25 } + \dfrac{ \left( y - 3 \right)^2}{ 4 } = 1 $$ | 2 |
113 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 4 \left( x - 1 \right)^2}{ \frac{ 3 }{ 2 } } + \dfrac{ \left( y - 2 \right)^2}{ 3 } = 1 $$ | 2 |
114 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 18 } + \dfrac{ \left( y - 2 \right)^2}{ 81 } = 1 $$ | 2 |
115 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 10 \right)^2}{ \frac{ 11 }{ 2 } } + \dfrac{ \left( y - 1 \right)^2}{ 3 } = 1 $$ | 2 |
116 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 4 \left( x - 3 \right)^2}{ 12 } + \dfrac{ 8 \left( y + 6 \right)^2}{ 20 } = 1 $$ | 2 |
117 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 10 x^2}{ 20 } + \dfrac{ y^2}{ 1200 } = 1 $$ | 2 |
118 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 8 \right)^2}{ 16 } + \dfrac{ \left( y - 5 \right)^2}{ 36 } = 1 $$ | 2 |
119 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y - 2 \right)^2}{ 16 } = 1 $$ | 2 |
120 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 17 }{ 10 } \right)^2}{ 6 } + \dfrac{ y^2}{ 15 } = 1 $$ | 2 |
121 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y - 5 \right)^2}{ 9 } = 1 $$ | 2 |
122 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 9 } + \dfrac{ \left( y + 5 \right)^2}{ 16 } = 1 $$ | 2 |
123 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 2 } + \dfrac{ y^2}{ 8 } = 1 $$ | 2 |
124 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ \left( y + 4 \right)^2}{ 4 } = 1 $$ | 2 |
125 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 169 } + \dfrac{ \left( y + 6 \right)^2}{ 100 } = 1 $$ | 2 |
126 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 13 } + \dfrac{ y^2}{ 2 } = 1 $$ | 2 |
127 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 5 \right)^2}{ 25 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 2 |
128 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 27 } + \dfrac{ y^2}{ 5 } = 1 $$ | 2 |
129 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 4 } + \dfrac{ \left( y + 5 \right)^2}{ 25 } = 1 $$ | 2 |
130 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 8 } = 1 $$ | 2 |
131 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 9x^2 + 25y^2 = 225 $$ | 2 |
132 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 9 } + \dfrac{ \left( y - 5 \right)^2}{ 25 } = 1 $$ | 2 |
133 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 169 } + \dfrac{ y^2}{ 25 } = 1 $$ | 2 |
134 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 54 } + \dfrac{ y^2}{ 3261 } = 1 $$ | 2 |
135 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 25 } = 1 $$ | 2 |
136 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 256 } + \dfrac{ y^2}{ 192 } = 1 $$ | 2 |
137 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 12x^2 + 15y^2 = 1 $$ | 2 |
138 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 9 } + \dfrac{ \left( y + 3 \right)^2}{ 4 } = 1 $$ | 2 |
139 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 9 } + \dfrac{ \left( y - 1 \right)^2}{ 16 } = 1 $$ | 2 |
140 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3261 } + \dfrac{ y^2}{ 54 } = 1 $$ | 2 |
141 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 169 } + \dfrac{ \left( y - 3 \right)^2}{ 25 } = 1 $$ | 2 |
142 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 3 } + \dfrac{ y^2}{ 54 } = 1 $$ | 2 |
143 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 25 } + \dfrac{ \left( y + 5 \right)^2}{ 9 } = 1 $$ | 2 |
144 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ \left( y + 1 \right)^2}{ 16 } = 1 $$ | 2 |
145 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 2 |
146 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 144 } + \dfrac{ \left( y - 4 \right)^2}{ 64 } = 1 $$ | 2 |
147 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 2 |
148 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 25 } + \dfrac{ \left( y - 8 \right)^2}{ 1 } = 1 $$ | 2 |
149 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 1 } + \dfrac{ \left( y + 1 \right)^2}{ 36 } = 1 $$ | 2 |
150 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 25 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 2 |