Question 1153740

given:

foci ({{{5}}},{{{0}}}), ({{{5}}},{{{0}}})

vertices ({{{3}}},{{{0}}}),  ({{{-3}}},{{{0}}})

We can tell that it is a horizontal hyperbola.

The center point is ({{{0}}}, {{{0}}}). 

To find {{{a}}}, we'll count from the center to either vertex. 

{{{a = 3}}}

To find {{{c}}}, we'll count from the center to either focus. 

{{{c = 5}}}

then use

{{{c^2 = a^2 + b^2}}}
{{{b^2 = c^2 -a^2}}}
{{{b^2 = 5^2 -3^2}}}
{{{b^2 = 25 -9}}}
{{{b^2 = 16}}}
{{{ b=4}}}


We have all our information:{{{ h = 0}}}, {{{k = 0}}}, {{{a = 3}}}, {{{b = 4}}}. Since it's a horizontal hyperbola centered in origin, we'll choose that formula and substitute in our information.


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


{{{drawing(600, 600, -10, 10, -10, 10, 
circle(-5,0,.12),circle(5,0,.12),circle(-3,0,.12),circle(3,0,.12),
locate(-5,0.5,F(-5,0)),locate(5,0.5,F(5,0)),
locate(-3,0.5,v(-3,0)),locate(3,0.5,v(3,0)),
 graph( 600, 600, -10, 10, -10, 10, -sqrt(16x^2/9-16), sqrt(16x^2/9-16))) }}}