Question

ellipses c:

Answer 1

Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by sixty four = 1

Answer 2

use the attached chart

Answer 3

\(\dfrac{x^2}{100} + \dfrac{y^2}{64} = 1\)

is same as :
\(\dfrac{x^2}{10^2} + \dfrac{y^2}{8^2} = 1\)

Answer 4

comparing it wid standard form :

\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\)

gives : \(a = 10, ~b = 8\)

Answer 5

see if u can use the chart to find out vertices/center/foci

Answer 6

how do you find the center? @ganeshie8

Answer 7

and also, how do you find c? @ganeshie8

Answer 8

center is (0, 0) for these ellipses...

Answer 9

these ellipses are centered at origin

Answer 10

use this for finding "c" :

c^2 = a^2 - b^2

Answer 11

so 100- 64= 36 which would be 6 okay so the verticies are -10,0 and 10,0 and the foci are -6,0 and 6,0 c: @ganeshie8

Answer 12

Excellent !

Answer 13

yay ^.^ if i post more questions like this will you help on thoses too c:

Answer 14

sure :)

Answer 15

but the attached chart is all u need... I see you're getting the hang of it :)

Answer 16

yay c: hold on how do you tell the difference of whether they are vertical or eliptical because the only difference is the denominator, which dosent tell me whether it is a or b

Answer 17

very good question !

Answer 18

whichever is largest is the \(\large a\)

Answer 19

\(\large a\) = length of semi-major axis

Answer 20

semi-major is axis is always alrger than the semi-minor axis

Answer 21

So, in short :
whatever denominator is LARGE is the \(\large a\)

Answer 22

ohh that makes sense c:

Answer 23

and how do you know when an ellipses isnt centered at the origin?

Answer 24

if the center is (h, k)
then the equation of ellipse wud look like :
http://www.teacherschoice.com.au/images/ellipse_types.gif

Answer 25

wait so this equation x squared divided by nine plus y squared divided by sixteen = 1 would be centered right?

Answer 26

@ganeshie8

Answer 27

do u mean it is centered at origin ?
then yes

Answer 28

any ellipse of form :

\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} =1\)

is centered at \((0,0)\)

Answer 29

yay c: thank you

Answer 30

:)