cuales son los puntos de i terseccion de una elipse y una hiperbola ... las ecuaciones están en la imagen
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![](https://es-static.z-dn.net/files/d1d/a4d195e60f8bed1d3eaa55d19c997293.jpg)
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Haber,
![\displaystyle \left \{ {{\frac{x^{2}}{49}+\frac{y^{2}}{24}=1} \atop {\frac{x^{2}}{16}-\frac{y^{2}}{9}=1}} \right. =\left \{ {{\frac{24x^{2}+49y^{2}}{1176}=1} \atop {\frac{9x^{2}-16y^{2}}{144}=1}} \right. = \left \{ {{24x^{2}+49y^{2}=1176} \atop {9x^{2}-16y^{2}=144}} \right. =\\\\...=\left \{ {{16(24x^{2}+49y^{2}=1176)} \atop {49(9x^{2}-16y^{2}=144)}} \right.=\left \{ {{384x^{2}+784y^{2}=18816} \atop {441x^{2}-784y^{2}=7056}} \right.=\\\\825x^{2}=25872\\x^{2}=\frac{784}{25}\\|x|=\sqrt{\frac{784}{25}} \displaystyle \left \{ {{\frac{x^{2}}{49}+\frac{y^{2}}{24}=1} \atop {\frac{x^{2}}{16}-\frac{y^{2}}{9}=1}} \right. =\left \{ {{\frac{24x^{2}+49y^{2}}{1176}=1} \atop {\frac{9x^{2}-16y^{2}}{144}=1}} \right. = \left \{ {{24x^{2}+49y^{2}=1176} \atop {9x^{2}-16y^{2}=144}} \right. =\\\\...=\left \{ {{16(24x^{2}+49y^{2}=1176)} \atop {49(9x^{2}-16y^{2}=144)}} \right.=\left \{ {{384x^{2}+784y^{2}=18816} \atop {441x^{2}-784y^{2}=7056}} \right.=\\\\825x^{2}=25872\\x^{2}=\frac{784}{25}\\|x|=\sqrt{\frac{784}{25}}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cleft+%5C%7B+%7B%7B%5Cfrac%7Bx%5E%7B2%7D%7D%7B49%7D%2B%5Cfrac%7By%5E%7B2%7D%7D%7B24%7D%3D1%7D+%5Catop+%7B%5Cfrac%7Bx%5E%7B2%7D%7D%7B16%7D-%5Cfrac%7By%5E%7B2%7D%7D%7B9%7D%3D1%7D%7D+%5Cright.+%3D%5Cleft+%5C%7B+%7B%7B%5Cfrac%7B24x%5E%7B2%7D%2B49y%5E%7B2%7D%7D%7B1176%7D%3D1%7D+%5Catop+%7B%5Cfrac%7B9x%5E%7B2%7D-16y%5E%7B2%7D%7D%7B144%7D%3D1%7D%7D+%5Cright.+%3D+%5Cleft+%5C%7B+%7B%7B24x%5E%7B2%7D%2B49y%5E%7B2%7D%3D1176%7D+%5Catop+%7B9x%5E%7B2%7D-16y%5E%7B2%7D%3D144%7D%7D+%5Cright.+%3D%5C%5C%5C%5C...%3D%5Cleft+%5C%7B+%7B%7B16%2824x%5E%7B2%7D%2B49y%5E%7B2%7D%3D1176%29%7D+%5Catop+%7B49%289x%5E%7B2%7D-16y%5E%7B2%7D%3D144%29%7D%7D+%5Cright.%3D%5Cleft+%5C%7B+%7B%7B384x%5E%7B2%7D%2B784y%5E%7B2%7D%3D18816%7D+%5Catop+%7B441x%5E%7B2%7D-784y%5E%7B2%7D%3D7056%7D%7D+%5Cright.%3D%5C%5C%5C%5C825x%5E%7B2%7D%3D25872%5C%5Cx%5E%7B2%7D%3D%5Cfrac%7B784%7D%7B25%7D%5C%5C%7Cx%7C%3D%5Csqrt%7B%5Cfrac%7B784%7D%7B25%7D%7D)
finalmente obtenemos que,
![x=\displaystyle\pm\frac{28}{5} x=\displaystyle\pm\frac{28}{5}](https://tex.z-dn.net/?f=x%3D%5Cdisplaystyle%5Cpm%5Cfrac%7B28%7D%7B5%7D)
con éste valor ya podemos obtener el valor de ye, eso te lo dejo para quelo termines...reemplaza
![\displaystyle\left \{ {{24x^{2}+49y^{2}=1176} \atop {9x^{2}-16y^{2}=144}} \right. \displaystyle\left \{ {{24x^{2}+49y^{2}=1176} \atop {9x^{2}-16y^{2}=144}} \right.](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cleft+%5C%7B+%7B%7B24x%5E%7B2%7D%2B49y%5E%7B2%7D%3D1176%7D+%5Catop+%7B9x%5E%7B2%7D-16y%5E%7B2%7D%3D144%7D%7D+%5Cright.)
en cualquiera de las dos y obtienes el valor ye
finalmente obtenemos que,
con éste valor ya podemos obtener el valor de ye, eso te lo dejo para quelo termines...reemplaza
en cualquiera de las dos y obtienes el valor ye
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