题目:已知双曲线C:x~2/a~2-y~2=1(a>0)的右焦点F,点A,B分别在C的两条渐近线上,AF⊥x轴,AB⊥OB,BF∥OA(O为坐标原点).(1)求双曲线C的方程;(2)过C上一点P(x_0y_0)(y_0≠0)的直线l:(x_0x)/a~2-y_0y=1与直线AF相交于点M,与直线x=3/2相交于点N,证明点P在C上移 Title: Known Hyperfocal C: Right Focus F of x: 2 ~ 2 / a ~ 2 ~ y ~ 2 = 1 (a> 0), Points A and B are on the two asymptotic lines of C, , AB ⊥ OB, BF ∥ OA (O is the origin of coordinates) (1) Find the equation of hyperbolic C; (2) Line l: (x_0x) / a ~ 2-y_0y = 1 intersects the straight line AF at point M and intersects the straight line x = 3/2 at point N, proving that point P moves up in C