Question

Does anybody know how to find the point of intersection between the ellipse: 3x^2+4y^2=3 and the parabola : 8y^2=9x

Answer 1

\[3x^2+4y^2=3\quad,\quad 8y^2=9x\]\[3x^2+\frac{9}{2}x=3\]\[x^2+\frac{3}{2}x-1=0\]\[x_{1,2}=\frac{-3/2\pm\sqrt{9/4+4}}{2}=\frac{-3/2\pm5/2}{2}=|_{-2}^{1/2}\]\[y^2=\frac{9}{8}x=\frac{9}{16}\quad,\quad y=\pm\frac{3}{4}\]\[\mbox{point of intersection: }\left(1/2,3/4\right),\left(1/2,-3/4\right)\] http://www.wolframalpha.com/input/?i=3x%5E2%2B4y%5E2%3D3+and+8y%5E2%3D9x