SOLUTION: Find the co-ordinates of the foci, the eccentricity and the equations of the directrices of the hyperbola 4x 2 — 9y2 = 36.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the co-ordinates of the foci, the eccentricity and the equations of the directrices of the hyperbola 4x 2 — 9y2 = 36.      Log On


   

Question 439715: Find the co-ordinates of the foci, the
eccentricity and the equations of the
directrices of the hyperbola 4x 2 — 9y2 = 36.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2+-+9y%5E2+=+36
x%5E2%2F9+-+y%5E2%2F4+=+1 after division by 36.
==> a%5E2+=+9 and b%5E2+=+4
Now b%5E2+=+c%5E2+-+a%5E2 for the hyperbola, and so c%5E2+=+9%2B4+=+13.
==> c+=+sqrt%2813%29.
==> The foci are (-sqrt%2813%29, 0) and (sqrt%2813%29, 0).
Now c = ae ==> e+=+c%2Fa+=+sqrt%2813%29%2F3, the eccentricity.
d+=+a%2Fe+=+3%2F%28sqrt%2813%29%2F3%29+=++9%2Fsqrt%2813%29==> the directrices are x+=+9%2Fsqrt%2813%29 and x+=+-9%2Fsqrt%2813%29