SOLUTION: Find the coordinates of the vertices and the foci and the length of the latus rectum of the hyperbola 16x^2 — 9y^2 =144.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the coordinates of the vertices and the foci and the length of the latus rectum of the hyperbola 16x^2 — 9y^2 =144.      Log On


   

Question 440072: Find the coordinates of the vertices and the
foci and the length of the latus rectum of
the hyperbola 16x^2 — 9y^2 =144.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Find the coordinates of the vertices and the foci and the length of the latus rectum 

16x^2 — 9y^2 =144

 x%5E2%2F9+-+y%5E2%2F16+=+1

Note: Standard Form of an Equation of an Hyperbola opening right and left is  

            %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 

where Pt(h,k) is a center  with vertices 'a' units right and left of center.

 x%5E2%2F9+-+y%5E2%2F16+=+1  C(0,0) with vertices V(-3,0) and V(3,0)

Domain {x| x ≤ -3 and x ≥ 3}  Range: 

Foci(c = sqrt%28a%5E2%2Bb%5E2%29+=+sqrt%2825%29=5): F(-5,0) and F(5,0)

The length of the Latus Rectum is 2b^2/a = 32/3