数学课前练习

1. 已知\(F_1(-1,0)\)，\(F_2(1,0)\)是椭圆\(C\)的两个焦点，过\(F_2\)且垂直\(x\)轴的直线交\(C\)于\(A\)，\(B\)两点，且\(|AB|=3\)，则\(C\)的方程为（）

A. \(\displaystyle \frac{x^2}{2} + y^2 = 1\)

B. \(\displaystyle \frac{x^2}{3} + \displaystyle \frac{y^2}{2} = 1\)

C. \(\displaystyle \frac{x^2}{4} + \displaystyle \frac{y^2}{3} = 1\)

D. \(\displaystyle \frac{x^2}{5} + \displaystyle \frac{y^2}{4} = 1\)

2. 若椭圆\(\displaystyle \frac{x^2}{a^2} + \displaystyle \frac{y^2}{3} = 1(a > \sqrt{3})\)的长半轴长等于其焦距，则\(a=\)（）

A. 2

B. \(2\sqrt{2}\)

C. \(2\sqrt{3}\)

D. 4