Question

Find the center, vertices, and foci of the ellipse with equation 2x2 + 7y2 = 14.

Answer 1

divide by 14
\[\frac{ \left( x-h \right)^{2} }{ a ^{2} }+\frac{ \left( y-k \right)^{2} }{ b ^{2} }=1\]
centre is (h,k)
\[b ^{2}=a ^{2}\left( 1-e ^{2} \right)\]
foci are (-ae,k) and (ae,k)

Answer 2

um to be honest I am not even really sure how to plug my equation into that @surjithayer

Answer 3

this is really confusing...

Answer 4

actually foci are (h-ae,k) and (h+ae,k)
vertices are (h-a,k) and (h+a,k)

Answer 5

let us start divide by14

Answer 6

\[\frac{ x ^{2} }{7 }+\frac{ y ^{2} }{2 }=1\]

Answer 7

here centre is (0,0)

Answer 8

\[a=\sqrt{7},b=\sqrt{2}\]

Answer 9

now you calculate e

Answer 10

\[2=7\left( 1-e ^{2} \right),\frac{ 2 }{7 }=1-e ^{2},e ^{2}=1-\frac{ 2 }{ 7 },e=\sqrt{\frac{ 5 }{ 7 }}\]

Answer 11

foci are (-ae,0) and (ae,0)
vertices are (-a,0) and (a,0)