7.已知F1,F2是椭圆$C:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$的左、右焦点,点P在椭圆C上,线段PF2与圆x2+y2=b2相切于点Q,且点Q为线段PF2的中点,则$\frac{{{a^2}+{e^2}}}{b}$(其中e为椭圆C的离心率)的最小值为( )
| A. | $\sqrt{6}$ | B. | $\frac{{3\sqrt{6}}}{4}$ | C. | $\sqrt{5}$ | D. | $\frac{{3\sqrt{5}}}{4}$ |
5.在区域$Ω=\left\{{(x,y)|\left\{\begin{array}{l}x≥0\\ x+y≤1\\ x-y≤1\end{array}\right.}\right\}$中,若满足ax+y>0的区域面积占Ω面积的$\frac{1}{3}$,则实数a的值是( )
| A. | $\frac{2}{3}$ | B. | $\frac{1}{2}$ | C. | $-\frac{1}{2}$ | D. | $-\frac{2}{3}$ |
4.已知函数f(x)=sin(x+φ)-2cos(x+φ)(0<φ<π)的图象关于直线x=π对称,则cos2φ=( )
| A. | $\frac{3}{5}$ | B. | $-\frac{3}{5}$ | C. | $\frac{4}{5}$ | D. | $-\frac{4}{5}$ |
3.已知数列{an}的前n项和为Sn,且${a_1}=1,{a_{n+1}}•{a_n}={2^n}(n∈{N^*})$,则S2016=( )
| A. | 3•21008-3 | B. | 22016-1 | C. | 22009-3 | D. | 22008-3 |
2.设F1,F2为双曲线$Γ:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$(a>0,b>0)的左、右焦点,P为Γ上一点,PF2与x轴垂直,直线PF1的斜率为$\frac{3}{4}$,则双曲线Γ的渐近线方程为( )
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| A. | y=±x | B. | $y=±\sqrt{2}x$ | C. | $y=±\sqrt{3}x$ | D. | y=±2x |