Question

15．已知拋物線(xiàn)y²=4x，直線(xiàn)y=x-1，求直線(xiàn)與拋物線(xiàn)的交點(diǎn)坐標(biāo)．

Answer 1

分析 聯(lián)立方程得$\left\{\begin{array}{l}{{y}^{2}=4x}&{①}\\{y=x-1}&{②}\end{array}\right.$，利用代入消元法即可解出．

解答 解：聯(lián)立方程得$\left\{\begin{array}{l}{{y}^{2}=4x}&{①}\\{y=x-1}&{②}\end{array}\right.$，
將②代入①（1）得：x²-6x+1=0，
解得：$x=3±2\sqrt{2}$，
代入②得：$y=2±2\sqrt{2}$，
∴$\left\{\begin{array}{l}{x=3+2\sqrt{2}}\\{y=2+2\sqrt{2}}\end{array}\right.$或$\left\{\begin{array}{l}{x=3-2\sqrt{2}}\\{y=2-2\sqrt{2}}\end{array}\right.$
∴直線(xiàn)與拋物線(xiàn)的交點(diǎn)坐標(biāo)為$（3+2\sqrt{2}，2+2\sqrt{2}）$或$（3-2\sqrt{2}，2-2\sqrt{2}）$．

點(diǎn)評(píng) 本題考查了代入消元法、直線(xiàn)與拋物線(xiàn)的交點(diǎn)坐標(biāo)求法，考查了推理能力與計(jì)算能力，屬于中檔題．