Ellipse – Solved Problems Database
All the problems and solutions shown below were generated using the Ellipse Calculator.
ID |
Problem |
Count |
151 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 25 } + \dfrac{ \left( y + 6 \right)^2}{ 36 } = 1 $$ | 2 |
152 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 9 } + \dfrac{ \left( y + 4 \right)^2}{ 16 } = 1 $$ | 2 |
153 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 16 } + \dfrac{ \left( y + 4 \right)^2}{ 25 } = 1 $$ | 2 |
154 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 49 } = 1 $$ | 2 |
155 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 2 \left( x + 10 \right)^2}{ \frac{ 9 }{ 2 } } + \dfrac{ 3 \left( y + \frac{ 41 }{ 10 } \right)^2}{ 12 } = 1 $$ | 2 |
156 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 1 } + \dfrac{ \left( y - 3 \right)^2}{ 4 } = 1 $$ | 2 |
157 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \sqrt{ 6 } } + \dfrac{ y^2}{ \sqrt{ 7 } } = 1 $$ | 2 |
158 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 2 \left( x + 4 \right)^2}{ 1 } + \dfrac{ 4 \left( y + 2 \right)^2}{ 4 } = 1 $$ | 2 |
159 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 4 } = 1 $$ | 2 |
160 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 16 } = 1 $$ | 2 |
161 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 169 } + \dfrac{ \left( y - 5 \right)^2}{ 144 } = 1 $$ | 2 |
162 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 64 } + \dfrac{ \left( y - 4 \right)^2}{ 16 } = 1 $$ | 2 |
163 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 10 \right)^2}{ 121 } + \dfrac{ \left( y + 7 \right)^2}{ 49 } = 1 $$ | 2 |
164 | 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 |
165 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 7 \right)^2}{ 4 } + \dfrac{ \left( y + 3 \right)^2}{ 36 } = 1 $$ | 2 |
166 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ \frac{ 100 }{ 9 } } + \dfrac{ \left( y - 5 \right)^2}{ 20 } = 1 $$ | 2 |
167 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y + 10 \right)^2}{ 1 } = 1 $$ | 2 |
168 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 3y^2 = \frac{ 3 }{ 2 } $$ | 2 |
169 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 9 } + \dfrac{ \left( y - 3 \right)^2}{ 16 } = 1 $$ | 2 |
170 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 5 \right)^2}{ 4 } + \dfrac{ \left( y + 5 \right)^2}{ 9 } = 1 $$ | 2 |
171 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 1 }{ 4 } \right)^2}{ \frac{\sqrt{ 3 }}{ 6 } } + \dfrac{ \left( y + \frac{ 1 }{ 6 } \right)^2}{ \frac{ 1 }{ 3 } } = 1 $$ | 2 |
172 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y - 5 \right)^2}{ 25 } = 1 $$ | 2 |
173 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 144 } + \dfrac{ y^2}{ 169 } = 1 $$ | 2 |
174 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 25 } + \dfrac{ \left( y - 1 \right)^2}{ 16 } = 1 $$ | 2 |
175 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 2 |
176 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 6 \right)^2}{ 51 } + \dfrac{ \left( y - 6 \right)^2}{ 36 } = 1 $$ | 2 |
177 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 676 } + \dfrac{ y^2}{ 576 } = 1 $$ | 2 |
178 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ x^2 + 2y^2 = 3 $$ | 2 |
179 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 2 |
180 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 2 |
181 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 2 |
182 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 30 } + \dfrac{ y^2}{ 20 } = 1 $$ | 2 |
183 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 49 } = 1 $$ | 2 |
184 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 4 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 2 |
185 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 25 \left( x + 2 \right)^2}{ 72 } + \dfrac{ 16 \left( y - 2 \right)^2}{ 72 } = 1 $$ | 2 |
186 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 1 } = 1 $$ | 2 |
187 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 16 } + \dfrac{ \left( y + 5 \right)^2}{ 9 } = 1 $$ | 2 |
188 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 144 } + \dfrac{ y^2}{ 169 } = 1 $$ | 2 |
189 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 100 } = 1 $$ | 2 |
190 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 64 } + \dfrac{ \left( y - 4 \right)^2}{ 16 } = 1 $$ | 2 |
191 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 35 } = 1 $$ | 2 |
192 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 1 } + \dfrac{ \left( y + 5 \right)^2}{ \frac{ 1 }{ 4 } } = 1 $$ | 2 |
193 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 3 \right)^2}{ 45 } + \dfrac{ \left( y - 5 \right)^2}{ 9 } = 1 $$ | 2 |
194 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ 16 \left( x + 2 \right)^2}{ 144 } + \dfrac{ 9 \left( y + 1 \right)^2}{ 144 } = 1 $$ | 2 |
195 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 16 } + \dfrac{ \left( y + 1 \right)^2}{ 4 } = 1 $$ | 2 |
196 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 4 } + \dfrac{ y^2}{ 8 } = 1 $$ | 2 |
197 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ 16 } + \dfrac{ \left( y - 2 \right)^2}{ 4 } = 1 $$ | 2 |
198 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 25 } + \dfrac{ \left( y - 4 \right)^2}{ 9 } = 1 $$ | 2 |
199 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 1 \right)^2}{ 9 } + \dfrac{ \left( y + 2 \right)^2}{ 25 } = 1 $$ | 2 |
200 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + \frac{ 19 }{ 5 } \right)^2}{ \frac{ 225 }{ 4 } } + \dfrac{ \left( y - 6 \right)^2}{ \frac{ 121 }{ 4 } } = 1 $$ | 2 |