Question 1199124


{{{9x^2+36y^2=324}}}

{{{9x^2/324+36y^2/324=324/324}}}

{{{x^2/36+y^2/9=1}}}

so
 center at ({{{0}}}, {{{0}}}), =>{{{h=0}}},{{{k=0}}}
{{{a=6}}}
{{{b=3}}}
{{{c=sqrt(6^2-3^2)=sqrt(27)=3sqrt(3)}}}

since a focus is at ({{{h-c}}}, {{{k}}})=>a foci are at ({{{3sqrt(3)}}},{{{0}}}) and  ({{{-3sqrt(3)}}},{{{0}}})

 eccentricity 

{{{e=c/a=3sqrt(3)/6=(1/2)sqrt(3)}}}


answer:
C)