抛物线y^2=8x焦点为F,倾斜角为锐角的直线L经过F,与抛物线相交A,B点...答:y² = 2px = 8x, p = 4, F(2, 0)倾斜角为锐角, 不妨取右上方, 左下方的交点为A(a²/8, a), B(b²/8, b), a > 0, b < 0 F是线AB一个3等分点, |AF| = 2|FB| (a²/8 - 2) = 2(2 - b²/8)(a - 0) = 2(0 - b)联立得a ...
设抛物线C:y^2=8x的焦点为F,准线与x轴相交于点K,点A在抛物线C上且|A...答:设点A的坐标为(x,y)满方程:y^2=8x.(1)由|AK|=√2|AF|,则,|AK|^2=2|AF|^2,即:(x+2)^2+y^2=2(x+2)^2.(2)由(1)(2)联合解得:x=2,y=4,故 A(2,4)由抛物线方程y^2=8x知,焦点坐标为F(2,0)K 的坐标为 K(-2,0)则三角形AFK的边:|AK|=4√2 ,|KF|...