Question

若双曲线x2/a2-y2/b2=-1的离心率为5/4,则两条渐近线的方程为？

Answer 1

即y²/b²-x²/a²=1
所以e²=c²/b²=25/16
c²=a²+b²
所以a²=9b²/16
b²/a²=9/16
b/a=3/4
所以是y=±3x/4

Answer 2

(1)X^3-9X
=X(X^2-9)
=X(X+3)(X-3)

(2)16X^4-1
=(4X^+1)(4X^2-1)
=(4X^2+1)(2X+1)(2X-1)

(3)6XY^2-9X^2Y-Y^3
=-Y(9X^2-6XY+Y^2)
=-Y(3X-Y)^2

(4) (2A-B)^2+8AB
=4A^2-4AB+B^2+8AB
=4A^2+4AB+B^2
=(2A+B)^2