知双曲线x²/a²-y²/b²=1(a>0,b>0)的两条渐近线与抛物线y²=2px(p>0)的准线分别交于A,B两点,O为坐标原点,若双曲线的离心率为2,△AOB的面积为根号3,则p=
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![知双曲线x²/a²-y²/b²=1(a>0,b>0)的两条渐近线与抛物线y²=2px(p>0)的准线分别交于A,B两点,O为坐标原点,若双曲线的离心率为2,△AOB的面积为根号3,则p=](/uploads/image/z/10190227-67-7.jpg?t=%E7%9F%A5%E5%8F%8C%E6%9B%B2%E7%BA%BFx%26%23178%3B%2Fa%26%23178%3B-y%26%23178%3B%2Fb%26%23178%3B%3D1%EF%BC%88a%3E0%2Cb%3E0%29%E7%9A%84%E4%B8%A4%E6%9D%A1%E6%B8%90%E8%BF%91%E7%BA%BF%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BFy%26%23178%3B%3D2px%28p%EF%BC%9E0%EF%BC%89%E7%9A%84%E5%87%86%E7%BA%BF%E5%88%86%E5%88%AB%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2CO%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%2C%E8%8B%A5%E5%8F%8C%E6%9B%B2%E7%BA%BF%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E4%B8%BA2%2C%E2%96%B3AOB%E7%9A%84%E9%9D%A2%E7%A7%AF%E4%B8%BA%E6%A0%B9%E5%8F%B73%2C%E5%88%99p%3D)
知双曲线x²/a²-y²/b²=1(a>0,b>0)的两条渐近线与抛物线y²=2px(p>0)的准线分别交于A,B两点,O为坐标原点,若双曲线的离心率为2,△AOB的面积为根号3,则p=
知双曲线x²/a²-y²/b²=1(a>0,b>0)的两条渐近线与抛物线y²=2px(p>0)的准线分别交于A,B两点,O为坐标原点,若双曲线的离心率为2,△AOB的面积为根号3,则p=
知双曲线x²/a²-y²/b²=1(a>0,b>0)的两条渐近线与抛物线y²=2px(p>0)的准线分别交于A,B两点,O为坐标原点,若双曲线的离心率为2,△AOB的面积为根号3,则p=
渐近线x²/a²-y²/b² = 0,y = ±bx/a
准线x = -p/2
A(-p/2,bp/(2a)),B(-p/2,-bp/(2a))
|AB| = bp/a
S = (1/2)*(bp/a)(p/2) = bp²/(4a) = √3
p² = 4√3a/b
e² = 4 = c²/a² = (a² + b²)/a² = 1 + b²/a²
b/a = √3
p² = 4√3/√3 = 4
p = 2