Question

What is the equation of the ellipse with foci (-10, 0), (10, 0) and co-vertices (0, -3), (0, 3). (I was never taught this, please help!)

Answer 1

since the foci are simetrical the center of the ellipse is the middle point between the foci

Answer 2

in this case is quite easy. the center is (0,0)

Answer 3

so the equation u r looking for is like this
\[ \large \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \]

Answer 4

b is the distance fro the center to either of the co-vertices
can u find b?

Answer 5

i honestly do not know how to do any of this

Answer 6

ok just for future references. if u r given two point \(P(a,b)\) and \(Q(c,d)\) then the distance between these is
\[ \large d(P,Q)=\sqrt{(a-c)^2+(b-d)^2} \]

Answer 7

beforre going on i have a question for u:

how come u have to do excercises on something u've never been taught?

Answer 8

It's an online program I have to do for credit recovery so Conic Sections was thrown in there and I was never taught that unit in my regular high school class

Answer 9

oh interesting
i was just curious. sorry.

did u understand the formula i posted

Answer 10

then your center is C(0,0) and one of the co-vertice is W1(0,3) then
\[ \large b=d(C,W_1)=\sqrt{(0-0^2+(0-3)^2}=3 \]

Answer 11

so far
\[ \large \frac{x^2}{a^2}+\frac{y^2}{3^2}=1 \]

Answer 12

yeah it's okay. I understood the formula I'm just trying to practice it now

Answer 13

now \(a\) is the distance from the center to either of the vertices
but we don't have the vertices so we have to use the following relation
\[ \large a^2-c^2=b^2 \]
where \(c\) is the distance between the center and either of the foci.
find this distance

Answer 14

Hello @SimplyLynn ???

Answer 15

sorry my laptop froze :/

Answer 16

lets finish this
\[ \large c=\sqrt{(0-10)^2+(0-0)^2}=10 \]
then
\[ \large a^2-c^2=b^2 \]
becomes
\[ \large a^2-10^2=3^2 \]
\[ \large a^2=9+100=109 \]

Answer 17

so finally
\[ \large \frac{x^2}{109}+\frac{y^2}{9}=1 \]

Answer 18

so when we don't have the vertices given we use \[a ^{2}-c ^{2}=b ^{2}\] ?

Answer 19

yes
when u don't have either the vertices, or the co-vertices, or the foci, u use that equation

Answer 20

okay, got it, thank you for your help and time :)

Answer 21

u r welcome
good luck with your on-line course

Answer 22

thanks :)