作业帮数学一道抛物线的题.求详解
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数学一道抛物线的题.求详解
数学一道抛物线的题.求详解
数学一道抛物线的题.求详解
F(p/2,0)
l:x = -p/2
显然F为的BC中点,B(b,c)在x轴下方,(b - p/2)/2 = p/2,b = 3p/2
c = -√3p
C(-p/2,√3p)
BC的斜率k = (√3p + √3p)/(-p/2 - 3p/2) = -√3
BC的方程:y = -√3(x - p/2)
代入y² = 2px,12x² - 20px + 3p² = 0
(6x - p)(2x - 3p) = 0
x = p/6 (舍去x = 3p/2,点B)
A(p/6,p/√3)
AF² = (p/6 - p/2)² + ( p/√3 - 0)²
p = 12
A(2,4√3),K(-6,4√3),F(6,0)
S = (1/2)*KA*A的纵坐标
= 16√3