Question

Help please. I'll give a medal and become a fan! Find the foci of this ellipse equation. 4x^2+9y^2=36.

Answer 1

lol no one likes these conic section questions
but that are not that bad
first divide everything by 36

Answer 2

\[\frac{x^2}{9}+\frac{y^2}{4}=1\]

Answer 3

which looks a lot like \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]

Answer 4

you good from there?
center is \((0,0)\) for example and since \(3^2=9\) the vertices are at \((-3,0)\) and \((3,0)\)

Answer 5

oh you need the foci also
that is ok because we have \(a=3\) and \(b=2\) so what is missing is \(c\) and \(c^2=a^2-b^2\)

Answer 6

So to find the foci I do
c^2=a^2-b^2
c^2=9^2-4^2
c^2=81-16
c^2=65
?

Answer 7

no

Answer 8

\[c^2=a^2-b^2\\
c^2=9-4\\
c^2=5\]

Answer 9

your denominators are the \(a^2\) and \(b^2\) you don't square them again

Answer 10

oh okay.

Answer 11

i always get confused with that

Answer 12

before we finish, is it clear that the center is \((0,0)\) ?

Answer 13

yes

Answer 14

ok you need to know the center to find the foci
you also need to know something else

Answer 15

is it the one on the left, or the one on the right?

Answer 16

I believe it's the second one. I hope.

Answer 17

yes, and you know that because in \[\frac{x^2}{9}+\frac{y^2}{4}=1\] the larger number is under the \(x\)

Answer 18

awesome!

Answer 19

but you need that because now you know the foci are \(\sqrt5\) units to the RIGHT AND LEFT of the center, not UP and DOWN

Answer 20

ok

Answer 21

and now we are done right?

Answer 22

i believe so.

Answer 23

(+/- square root 5, 0)?

Answer 24

Thanks @satellite73