hyperbola conics question (1 Viewer)

[kr73114]

1) find the equation of a hyperbola with foci (10,0) and (-10,0) and asymptotes y=4x/3 and y=-4x/3
2)find the equation of a hyperbola with eccentricity 5/4, focus (-10,0) and
directrix x=-32/5
thanks

 

[ninetypercent]

1) foci are on x axis.
ae = 10
b/a = 4/3

b^2 = a^2(e^2-1)
b^2/a^2 = e^2 - 1
16/9 + 1 = e^2
25/9 = e^2
e = 5/3 (e>0)

a = 10/e
= 6

b/6 = 4/3
b = 4/3 x 6
= 8

equation is x^2/36 - y^2/64 = 1

 

[ninetypercent]

haven't touched this stuff in agessssss. I'm starting to forget. correct me if i am wrong LOL

 

[ninetypercent]

2) find the equation of a hyperbola with eccentricity 5/4, focus (-10,0) and
directrix x=-32/5

ae = 10
a x 5/4 = 10
a = 10 x 4/5
= 8

a^2 = b^2(e^2-1)
64 = b^2(25/16-1)
64 = b^2 (9/16)
b^2 = 64 x 16/9
b = 32/3 (i think) didn't use calculator

and then plug into equation

 

[kr73114]

2) find the equation of a hyperbola with eccentricity 5/4, focus (-10,0) and
directrix x=-32/5

ae = 10
a x 5/4 = 10
a = 10 x 4/5
= 8

a^2 = b^2(e^2-1)
64 = b^2(25/16-1)
64 = b^2 (9/16)
b^2 = 64 x 16/9
b = 32/3 (i think) didn't use calculator

and then plug into equation

thanks