(1)焦點在X軸上,虛軸長為12,離心率為5/4?
(2)頂點間的'距離為6,漸近線方程為y=+3/2x或-3/2x?
解:
(1)設雙曲線方程為x^2/a^2 - y^2/b^2 = 1(a0)
根據題意2b=12,b=6 b^2=36
∵e^2 = c^2/a^2
=(a^2 + b^2 )/ a^2
=(a^2 + 36)/ a^2
= 25 / 16
a^2 = 64 雙曲線方程為x^2/64 - y^2/36 = 1
(2)設雙曲線方程為x^2/a^2 - y^2/b^2 = 1(a0)
或y^2/a^2 - x^2/b^2 = 1(a0)
∵頂點間的距離為6 2a=6 a=3 a^2 = 9
∵漸近線方程為y=(3/2)x
y=(b/a)x=(3/2)x 或 y=(a/b)x=(3/2)x
b=9/2 b^2 = 81/4 或 b=2 b^2=4
雙曲線方程為x^2/9 - 4y^2/81 = 1 或 y^2/9 - x^2/4 = 1