抛物线y的平方=4x的准线与双曲线x²/a²-y²/4=1交与A,B两点,f是抛物线焦点,fab是正三角形,求离心率
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 14:15:11
![抛物线y的平方=4x的准线与双曲线x²/a²-y²/4=1交与A,B两点,f是抛物线焦点,fab是正三角形,求离心率](/uploads/image/z/6550975-55-5.jpg?t=%E6%8A%9B%E7%89%A9%E7%BA%BFy%E7%9A%84%E5%B9%B3%E6%96%B9%3D4x%E7%9A%84%E5%87%86%E7%BA%BF%E4%B8%8E%E5%8F%8C%E6%9B%B2%E7%BA%BFx%26%23178%3B%EF%BC%8Fa%26%23178%3B-y%26%23178%3B%2F4%3D1%E4%BA%A4%E4%B8%8EA%2CB%E4%B8%A4%E7%82%B9%2Cf%E6%98%AF%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%84%A6%E7%82%B9%2Cfab%E6%98%AF%E6%AD%A3%E4%B8%89%E8%A7%92%E5%BD%A2%2C%E6%B1%82%E7%A6%BB%E5%BF%83%E7%8E%87)
抛物线y的平方=4x的准线与双曲线x²/a²-y²/4=1交与A,B两点,f是抛物线焦点,fab是正三角形,求离心率
抛物线y的平方=4x的准线与双曲线x²/a²-y²/4=1交与A,B两点,f是抛物线焦点,fab是正三角形,求离心率
抛物线y的平方=4x的准线与双曲线x²/a²-y²/4=1交与A,B两点,f是抛物线焦点,fab是正三角形,求离心率
y²=4x = 2px,p = 2
准线x = -1,F(1,0)
准线交x轴于C(-1,0)
CF = 2
tan∠AFC = tan30˚ = AC/CF = AC/2 = √3/3
AC = 2√3/3
A(-1,2√3/3)
代入x²/a²-y²/4=1,a² = 4/3
c² = a² + b² = 4/3 + 4 = 16/3
e = c/a = (4/√3)/(2/√3) = 2