Question

Find the equation of the ellipse given the foci (plus or minus 4, 0) ; minor axis is 6

Answer 1

@nincompoop @Directrix @mathmate

Answer 2

The definition of the ellipse:
a=major axis, b=minor axis, c=semi-focal distance.
By Pythagoras theorem, \(a^2=b^2+c^2.\)
The corresponding equation of the ellipse is
\(\Large \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Answer 3

so c^2=a^2-b^2
16=a^2-36
a^2=16+36
a^2=52
then the equation is \[\frac{ x^2 }{ 52 }+\frac{ y^2 }{ 36 }=1\]

Answer 4

am i correct?

Answer 5

hi!!

Answer 6

looks good sqrt(36)<sqrt(52)
so the minor axis is sqrt(36)
and the foci will lay on the major axis
and so we are basically given the major axis is the x-axis because (-4,0) and (4,0) are points that lay on the x-axis
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