1)3.8×0.15=0.870
2)1.04:2.6=0.4
3)0.870-0.4=0.470
4)0.470+0.83=1.300=1.3
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(m+4.8)+(-3.2-m)=m+4.8-3.2-m=1.6
Пусть
, тогда
![\Big||x+i(y-2)|-|x+i(y+2)|\Big|=3\\ \\ \Big|\sqrt{x^2+(y-2)^2}-\sqrt{x^2+(y+2)^2}\Big|=3](https://tex.z-dn.net/?f=%5CBig%7C%7Cx%2Bi%28y-2%29%7C-%7Cx%2Bi%28y%2B2%29%7C%5CBig%7C%3D3%5C%5C%20%5C%5C%20%5CBig%7C%5Csqrt%7Bx%5E2%2B%28y-2%29%5E2%7D-%5Csqrt%7Bx%5E2%2B%28y%2B2%29%5E2%7D%5CBig%7C%3D3)
Возводим обе части уравнения в квадрат, получим
![x^2+(y-2)^2-2\sqrt{x^2+(y+2)^2}\sqrt{x^2+(y-2)^2}+x^2+(y+2)^2=9\\ \\ 2x^2+2y^2-1=2\sqrt{\Big(x^2+(y-2)^2\Big)\Big(x^2+(y+2)^2\Big)}](https://tex.z-dn.net/?f=x%5E2%2B%28y-2%29%5E2-2%5Csqrt%7Bx%5E2%2B%28y%2B2%29%5E2%7D%5Csqrt%7Bx%5E2%2B%28y-2%29%5E2%7D%2Bx%5E2%2B%28y%2B2%29%5E2%3D9%5C%5C%20%5C%5C%202x%5E2%2B2y%5E2-1%3D2%5Csqrt%7B%5CBig%28x%5E2%2B%28y-2%29%5E2%5CBig%29%5CBig%28x%5E2%2B%28y%2B2%29%5E2%5CBig%29%7D)
Снова возводя в квадрат и выполняя преобразования, мы получим
![36x^2-28y^2+63=0\\ \\ \dfrac{x^2}{(\frac{\sqrt{63}}{6})^2}-\dfrac{y^2}{(\frac{\sqrt{63}}{\sqrt{28}})^2}=-1](https://tex.z-dn.net/?f=36x%5E2-28y%5E2%2B63%3D0%5C%5C%20%5C%5C%20%5Cdfrac%7Bx%5E2%7D%7B%28%5Cfrac%7B%5Csqrt%7B63%7D%7D%7B6%7D%29%5E2%7D-%5Cdfrac%7By%5E2%7D%7B%28%5Cfrac%7B%5Csqrt%7B63%7D%7D%7B%5Csqrt%7B28%7D%7D%29%5E2%7D%3D-1)
Это уравнение гиперболы, только действительная и мнимая полуоси лежат на оси ординат, т.е. сместили гиперболу вида
поворотом под углом 90°.
![c=\sqrt{a^2+b^2}=\sqrt{\left(\dfrac{\sqrt{63}}{6}\right)^2+\left(\dfrac{\sqrt{63}}{\sqrt{28}}\right)^2}=\sqrt{\dfrac{63}{36}+\dfrac{63}{28}}=\sqrt{4}=2](https://tex.z-dn.net/?f=c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%3D%5Csqrt%7B%5Cleft%28%5Cdfrac%7B%5Csqrt%7B63%7D%7D%7B6%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B%5Csqrt%7B63%7D%7D%7B%5Csqrt%7B28%7D%7D%5Cright%29%5E2%7D%3D%5Csqrt%7B%5Cdfrac%7B63%7D%7B36%7D%2B%5Cdfrac%7B63%7D%7B28%7D%7D%3D%5Csqrt%7B4%7D%3D2)
Тогда эксцентриситет: ![\varepsilon =\dfrac{c}{a}=\dfrac{2}{\frac{\sqrt{63}}{6}}=\dfrac{2\cdot6}{3\sqrt{7}}=\dfrac{4}{\sqrt{7}}](https://tex.z-dn.net/?f=%5Cvarepsilon%20%3D%5Cdfrac%7Bc%7D%7Ba%7D%3D%5Cdfrac%7B2%7D%7B%5Cfrac%7B%5Csqrt%7B63%7D%7D%7B6%7D%7D%3D%5Cdfrac%7B2%5Ccdot6%7D%7B3%5Csqrt%7B7%7D%7D%3D%5Cdfrac%7B4%7D%7B%5Csqrt%7B7%7D%7D)
Ответ:
.