Question 1136090

Find the center, vertices, and foci of the ellipse with equation 

{{{2x^2 + 9y^2 = 18}}}........both sides divide by {{{18}}}

{{{2x^2/18 + 9y^2/18 = 18/18}}}

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

=> {{{h=0}}}, {{{k=0}}},{{{a=sqrt(9)}}}=±{{{3}}}, {{{b=sqrt(2)}}}

center:({{{0}}},{{{0}}})


{{{c=sqrt(9-2)=sqrt(7)}}}


the vertices are at ({{{h+a}}},{{{k}}}), ({{{h-a}}}, {{{k}}} )

({{{0+3}}},{{{0}}})=({{{3}}},{{{0}}})
({{{0-3}}},{{{0}}})=({{{-3}}},{{{0}}})

({{{h+c}}},{{{k}}}), ({{{h-c}}}, {{{k}}} )

({{{0+sqrt(7)}}},{{{0}}})= ({{{sqrt(7)}}},{{{0}}})
({{{0-sqrt(7)}}}, {{{k}}} )=({{{-sqrt(7)}}},{{{0}}})




answer:
D.Center: (0, 0); Vertices: (-3, 0), (3, 0); Foci: Ordered pair negative square root seven comma zero and ordered pair square root seven comma zero