21．已知点 $A(2,1)$ 在双曲线 $C: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{a^{2}-1}=1(a>1)$ 上，直线 $l$ 交 $C$ 于 $P, Q$ 两点，直线 $A P, A Q$ 的斜率之和为 0 ．
（1）求 $l$ 的斜率；
（2）若 $\tan \angle P A Q=2 \sqrt{2}$ ，求 $\triangle P A Q$ 的面积．
直线的倾斜角与斜率 · 历年高考数学真题与解析
本页汇总 高考真题检索 的「直线的倾斜角与斜率」高考数学真题共 2 道，覆盖 2009–2022 年，最常出题型为 解答题；含完整答案与解析。
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4．（5分）（2009•陕西）过原点且倾斜角为 $60^{\circ}$ 的直线被圆 $x^{2}+y^{2}-4 y=0$ 所截得的弦长为（
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