Question

抛物线的顶点是坐标原点,对称轴是坐标轴,集点在X轴上,若直线L过焦点且垂直于X轴交抛

Answer 1

抛物线的顶点是坐标原点,对称轴是坐标轴,集点在X轴上,则抛物线可表达为y² =2px或y² = -2px,p >0

前者的焦点为(p/2,0),直线L:x = p/2

代入y² =2px,y² =2p*p/2= p²,y = ±p

A(p/2,-p),B(p/2,p)

|AB| = 2p=6

p = 3

y² = 6x

类似地,另一解为y² = -6x