六扇屏
幼苗
共回答了22个问题采纳率:86.4% 举报
答:
① 焦点x轴上设抛物线方程:y² = 2px判断焦点(p/2,0)点
② 设A点坐标(x1,y1),B点坐标(x2,y2)设AB斜率k线段AB垂直平分线斜率k'
则:kk' = -1所:
(y1-y2)/(x1-x2) * [(y1+y2)/2 - 0 ]/[(x1+x2)/2 - 6] = -1
(y1² - y2²) / [x1² - x2² -12(x1 - x2)] = -1
代入y1²=2px1,y2²=2px2化简:
2p/(x1 + x2 - 12) = -1
x1 + x2 = 12 - 2p ---
③
AF²=(x1 - p/2)² + y1² = (x1 - p/2)² + 2px1 = (x1 + p/2)²
AF = x1 + p/2
同理:
BF = x2 + p/2
AF + BF = x1 + x2 + p ---
link:
12 - 2p + p = 8
p=4
综上:
抛物线方程:
y² = 8x
1年前
1