SOLUTION: Please give explanation and steps for Find the vertices and asymptotes of the hyperbola given by the equation y^2/9 - x^2/16 = 1

 

Hi,

 C(0,0) opening Up and down along x = 0

Vertices: V(0,-3) and V(0,3)  units up and down from center

foci: F(0,-5) and F(0, 5)  || = 5 units up and down from center

Asymptotes: slopes  m =  ± 3/4,  thru (0,0), y =  ± (3/4)x 

Standard Form of an Equation of an Hyperbola opening up and down is:

   with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis

Foci units units up and down from center, along x = h

& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a