Question 1115786

 Given an ellipse: 

{{{x^2/36+y^2/32=1}}} 

This is the form of an ellipse. Use this form to determine the values used to find the center along with the major and minor axis of the ellipse.

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

so, {{{h=0}}}, {{{k=0}}}-> center is at  ({{{h}}},{{{k}}})=  ({{{0}}},{{{0}}})

{{{a^2=36}}}->{{{a=6}}} 

{{{b^2=32}}}->{{{b=4sqrt(2)}}} 

Find {{{c}}}, the distance from the center to a focus using following formula:

{{{c=sqrt(a^2-b^2)}}}

{{{c=sqrt(36-32)}}}

{{{c=sqrt(4)}}}

{{{c=2}}} or {{{c= -2}}} 

Find the foci:
the first focus of an ellipse can be found by adding {{{c}}} to {{{h}}}
.
({{{h+c}}},{{{k}}})=({{{2}}},{{{0}}})

the second foci

({{{h+c}}},{{{k}}})=({{{0+(-2)}}},{{{0}}})=({{{-2}}},{{{0}}})


the distance between the foci: 

{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}}

{{{d=sqrt((2-(-2))^2+(0-0)^2)}}}

{{{d=sqrt((2+2)^2)}}}

{{{d=sqrt(4^2)}}}

{{{d=4}}}