Question 1154219


The formula generally associated with the focus of an ellipse is {{{c^2=a^2-b^2}}} where {{{c}}} is the distance from the focus to center , {{{a}}} is the distance from the center to a vetex and {{{b}}} is the distance from the center to a co-vetex.

if foci at ({{{-9}}},{{{0}}}) and ({{{9}}},{{{0}}}), we know that {{{c=9}}} and center is at {{{origin}}}

if y​-intercepts are {{{-4}}} and {{{4}}}, co-vetices are at ({{{0}}},{{{-4}}}) and ({{{0}}},{{{4}}}) => {{{b=4}}}

use {{{c^2=a^2-b^2}}} to calculate {{{a}}}

{{{9^2=a^2-4^2}}}

{{{9^2+4^2=a^2}}}

{{{81+16=a^2}}}

{{{97=a^2}}}


formula you will need is

{{{x^2/a^2+y^2/b^2=1}}}...plug in {{{a^2}}} and {{{b^2}}}


{{{x^2/97+y^2/16=1}}}



{{{drawing ( 600, 600, -10, 10, -10, 10,

circle(0,-4,.12), circle(0,4,.12), circle(9,0,.12),circle(-9,0,.12),

locate(0,-4,cv(0,-4)),locate(0,4,cv(0,4)), locate(9,0.5,f(9,0)), locate(-9,0.5,f(-9,0)),
graph( 600, 600, -10, 10, -10, 10,-sqrt(16(1-x^2/97)) ,sqrt(16(1-x^2/97)))) }}}