Question 1185036
the standard form of the equation of the hyperbola with;

1. 

{{{F[1]}}} ({{{5}}},{{{0}}}), {{{F[2]}}} ({{{-5}}},{{{0}}})

{{{F[1]}}} ({{{c}}},{{{0}}})=>{{{c=5}}}

{{{V[1]}}} ({{{4}}},{{{0}}}), {{{V[2]}}} ({{{-4}}},{{{0}}})

{{{V[1]}}} ({{{a}}},{{{0}}}) =>{{{a=4}}}

{{{b^2=c^2-a^2}}}
{{{b^2=5^2-4^2}}}
{{{b^2=25-16}}}
{{{b^2=9}}}

=>{{{b=3}}}

=> Co-vertices: ({{{0}}},{{{-3}}}), ({{{0}}},{{{3}}})
=> center is at origin

Major (transverse) axis length: distance between vertices{{{2a=8 }}}
Semi-major axis length: {{{a=4}}}
Minor (conjugate) axis length: {{{2b=6}}}
Semi-minor axis length:{{{ b=3}}}

equation of the hyperbola: 

{{{x^2/4^2-y^2/3^2=1}}}

{{{x^2/16-y^2/9=1}}}


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-5,0,.12),circle(5,0,.12),circle(-4,0,.12),circle(4,0,.12),
locate(-5,0.7,F(-5,0)),locate(5,0.7,F(5,0)),
locate(-4,0.5,V(-4,0)),locate(4,0.5,V(4,0)),
 graph( 600, 600, -10, 10, -10, 10, sqrt(9(x^2/16-1)), -sqrt(9(x^2/16-1)))) }}}