Question 440072
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
Find the coordinates of the vertices and the foci and the length of the latus rectum 
16x^2 — 9y^2 =144
 {{{x^2/9 - y^2/16 = 1}}}
Note: Standard Form of an Equation of an Hyperbola opening right and left is  
            {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} 
where Pt(h,k) is a center  with vertices 'a' units right and left of center.
 {{{x^2/9 - y^2/16 = 1}}}  C(0,0) with vertices V(-3,0) and V(3,0)
Domain {x| x &#8804; -3 and x &#8805; 3}  Range:*[tex \large \ \ y\ \in\ \mathbb{R}] 
Foci(c = {{{sqrt(a^2+b^2) = sqrt(25)=5}}}): F(-5,0) and F(5,0)
The length of the Latus Rectum is 2b^2/a = 32/3
 
{{{drawing(300,300,-10,10,-10,10,  grid(1),
circle(0, 0,0.3),
circle(-3, 0,0.3),
circle(3, 0,0.3),
circle(-5, 0,0.3),
circle(5, 0,0.3),
graph(300,300,-10,10,-10,10,0,4sqrt(((x)^2/9) -1),-4sqrt(((x)^2/9) -1)))}}}