两道数学题，双曲线

7.e=c/a
渐近线y=±b/a*x
tanα=b/a
cosα=a/√(a^2+b^2)=a/c=1/e∈[1/2,√3/2]
α∈[π/6,π/3]
8.P是x^2/a^2-y^2/b^2=1与圆x^2+y^2=c^2的交点
x^2/a^2-y^2/b^2=1
x^2+y^2=c^2=a^2+b^2
x^2/a^2-(c^2-x^2)/b^2=1
即x^2(1/a^2+1/b^2)-c^2/b^2=1
即(a^2+b^2)/(a^2b^2)*x^2-c^2/b^2=1
即(c^2/a^2)*x^2/b^2-c^2/b^2=1
(e^2*x^2-c^2)/b^2=1 (1)
S=(1/2)(ex-a)(ex+a)=9 (两焦半径之积的1/2)
即e^2*x^2-a^2=18
即e^2*x^2=18+a^2 (2)
(2)代入(1)得
(18+a^2-c^2)/b^2=1
(18-b^2)/b^2=1
b^2=9 b=3
c^2-a^2=9 (3)
c/a=5/4 (4)
联立(3)(4) a=4 c=5
a+b=3+4=7