Question 1134791


The standard form of a hyperbola that opens sideways is 

{{{(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1}}}


if center at​ ({{{0}}},{{{0}}}), means {{{h=0}}} and {{{k=0}}} and your equation is


{{{x^2 / a^2 - y^2 / b^2 = 1}}}


if {{{a=4​}}}, 

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

if {{{e=4​}}}, horizontal focal axis

{{{e=c/a}}}
{{{4=c/4}}}
{{{c=16}}}

since {{{c=sqrt(a^2+b^2)}}}...plug in {{{a=4}}}​, {{{c=16}}} and solve for {{{b}}}

{{{16=sqrt(16+b^2)}}}.......square both sides

{{{16^2=(sqrt(16+b^2))^2}}}

{{{256=16+b^2}}}

{{{b^2=256-16}}}

{{{b^2=240}}}

{{{b=4sqrt(15)}}}


and your equation is

{{{x^2 / 16 - y^2 / 240 = 1}}}