(1)∵A(a,0),B(0,-b),∴设直线AB:-=1 ∴,∴, ∴双曲线方程为:-=1. (2)∵双曲线方程为:-=1, ∴A1(-,0),A2(,0),设P(x0,y0), ∴kPA1=,kPA2=, ∴k1k2===3. B(0,-3)B1(0,3),设M(x1,y1),N(x2,y2) ∴设直线l:y=kx-3, ∴, ∴3x2-(kx-3)2=9. (3-k2)x2+6kx-18=0, ∴x1+x2= y1+y2=k(x1+x2)-6=x1x2= y1y2=k2(x1x2)-3k(x1+x2)+9
| ∵•=0 | ∴x1x2+y1y2-3(y1+y2)+9=0 | +9-+9=0 |
| |
k2=5,即k=±代入(1)有解, ∴lMN:y=±x-3. |