Question 1176239
Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

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

center is at ({{{0}}},{{{0}}})

Foci: ({{{5}}},{{{ 0}}}), ({{{-5}}}, {{{0}}})

focus is {{{5}}} units from the center, so {{{c = 5}}} and 

major axis of length {{{2a=14}}}->{{{a=7}}}

use the equation {{{b^2 + c^2 = a^2}}} to find {{{b^2}}}

{{{b^2  = a^2-c^2}}}
{{{b^2  = 7^2-5^2}}}
{{{b^2  = 49-25}}}
{{{b^2  = 24}}}

your equation is:

{{{x^2/49+y^2/24=1}}}


{{{ drawing( 600, 600, -10, 10, -10, 10,
circle(-5,0,.12),locate(-5,0.5,F(-5,0)),
circle(5,0,.12),locate(5,0.5,F(5,0)),
graph( 600, 600, -10, 10, -10, 10,  -(2/7)sqrt(6)*sqrt(49-x^2), (2/7) sqrt(6)*sqrt(49 -x^2)))) }}}