Question

Find the center, vertices, and foci of the ellipse with equation 5x2 + 8y2 = 40.

Answer 1

@paki @phi

Answer 2

@ganeshie8

Answer 3

do you know the conics formula to find these?

Answer 4

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

Answer 5

\[5x^{2} + 8y^{2} = 40\]
you want the right side =1, so divide both sides by 40.
\[\frac{ 5x^{2} }{ 40 } + \frac{ 8y^{2} }{ 40 } = \frac{ 40 }{ 40 }\]
\[\frac{ x^{2} }{ 8 } + \frac{ y^{2} }{ 5 } = 1\]

Answer 6

Now,
\[a^{2} = 8 , b^2= 5\]
\[a= 2\sqrt{2} ,
b = \sqrt{5}\]

Answer 7

from here on, you can use this equation sheet to find foci, vertices, and center.

Look under the section Ellipse, on the left side.
https://www20.csueastbay.edu/library/scaa/files/pdf/Conics.pdf

Answer 8

foci= (c,0) , (-c,0)

so we need to find c

\[c^{2} = a^{2} -b^{2}\]
\[c^{2} = 8-5\]
\[c= \sqrt{3}\]

Answer 9

thank you

Answer 10

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