若椭圆X²÷a²+y²÷b²=1(a>b>0)的左右焦点为F1和F2椭圆的离心率为根号2:2椭圆X²÷a²+y²÷b²=1(a>b>0)的焦点为F1和F2椭圆的离心率为根号2:2求过点c(-1,0)且斜率为K的直
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![若椭圆X²÷a²+y²÷b²=1(a>b>0)的左右焦点为F1和F2椭圆的离心率为根号2:2椭圆X²÷a²+y²÷b²=1(a>b>0)的焦点为F1和F2椭圆的离心率为根号2:2求过点c(-1,0)且斜率为K的直](/uploads/image/z/1012639-31-9.jpg?t=%E8%8B%A5%E6%A4%AD%E5%9C%86X%26%23178%3B%C3%B7a%26%23178%3B%2By%26%23178%3B%C3%B7b%26%23178%3B%3D1%28a%EF%BC%9Eb%EF%BC%9E0%EF%BC%89%E7%9A%84%E5%B7%A6%E5%8F%B3%E7%84%A6%E7%82%B9%E4%B8%BAF1%E5%92%8CF2%E6%A4%AD%E5%9C%86%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E4%B8%BA%E6%A0%B9%E5%8F%B72%3A2%E6%A4%AD%E5%9C%86X%26%23178%3B%C3%B7a%26%23178%3B%2By%26%23178%3B%C3%B7b%26%23178%3B%3D1%28a%EF%BC%9Eb%EF%BC%9E0%EF%BC%89%E7%9A%84%E7%84%A6%E7%82%B9%E4%B8%BAF1%E5%92%8CF2%E6%A4%AD%E5%9C%86%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E4%B8%BA%E6%A0%B9%E5%8F%B72%3A2%E6%B1%82%E8%BF%87%E7%82%B9c%28-1%2C0%29%E4%B8%94%E6%96%9C%E7%8E%87%E4%B8%BAK%E7%9A%84%E7%9B%B4)
若椭圆X²÷a²+y²÷b²=1(a>b>0)的左右焦点为F1和F2椭圆的离心率为根号2:2椭圆X²÷a²+y²÷b²=1(a>b>0)的焦点为F1和F2椭圆的离心率为根号2:2求过点c(-1,0)且斜率为K的直
若椭圆X²÷a²+y²÷b²=1(a>b>0)的左右焦点为F1和F2椭圆的离心率为根号2:2
椭圆X²÷a²+y²÷b²=1(a>b>0)的焦点为F1和F2椭圆的离心率为根号2:2求过点c(-1,0)且斜率为K的直线l交椭圆于A,B两点,若AC=2CB,则△OAB面积最大时,求椭圆的方程
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若椭圆X²÷a²+y²÷b²=1(a>b>0)的左右焦点为F1和F2椭圆的离心率为根号2:2椭圆X²÷a²+y²÷b²=1(a>b>0)的焦点为F1和F2椭圆的离心率为根号2:2求过点c(-1,0)且斜率为K的直
c/a=√2/2,
∴a^=2c^,b^=c^,
∴椭圆方程是x^+2y^=2c^,
AC=2CB,
∴设B(-1+m,n),A(-1-2m,-2n),于是
(-1+m)^+2n^=2c^,①
(-1-2m)^+8n^=2c^,②
①*4-②,3-12m=6c^,m=(1-2c^)/4,
代入①,(9+12c^+4c^4)/16+2n^=2c^,
n^=(-9+20c^-4c^4)/32=[-(c^-5/2)^+4]/8,
当c^=5/2时最大,
|AB|=3√(m^+n^),
AB:y=n(x+1)/m,即nx-my+n=0,
O到AB的距离d=|n|/√(m^+n^),
∴S△OAB=(1/2)|AB|d=(3/2)|n|,当c^=5/2时最大,
∴所求椭圆方程是x^+2y^=5,即x^/5+y^/2.5=1.