SOLUTION: find the foci, vertices and length of the two axis of the hyperbola 5x^2-4y^2=80

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: find the foci, vertices and length of the two axis of the hyperbola 5x^2-4y^2=80      Log On


   

Question 752412: find the foci, vertices and length of the two axis of the hyperbola
5x^2-4y^2=80
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
form of horizontal hyperbola:
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
.
5x%5E2-4y%5E2=80
5x%5E2%2F80+-+4y%5E2%2F80=1
x%5E2%2F8+-+y%5E2%2F20=1
x%5E2%2F%282sqrt%282%29%29%5E2+-+y%5E2%2F%282sqrt%285%29%29%5E2+=+1
a=2sqrt%282%29
b=2sqrt%285%29
8 + 20 = c^2
28 = c^2
2sqrt%287%29 = c
.
vertex:
(0,0)
.
foci:
(0,+-2sqrt%287%29)
.
asymptotes:
y = +-(b/a)x
y = +-sqrt%285%29%2Fsqrt%282%29x
y = +-sqrt%2810%29%2F2x