Question

Conic sections help!

Answer 1

(x-5)^2/4+(y+3)^2/16=1

Answer 2

need to find vertices, foci, eccentricity, length of major and minor axis

Answer 3

HI
you know what shape this is?

Answer 4

yes a circle and its center is (5,-3)

Answer 5

if you know the shape, and the center , the rest its easy
no, it is not a circle

Answer 6

although you did get the center right

Answer 7

an oval?

Answer 8

yeah
which math teacher call "ellipse"

Answer 9

ok yeah i know what that is

Answer 10

so you got the center, next question is this

Answer 11

yes

Answer 12

which one ?

Answer 13

the vertical one

Answer 14

yes

Answer 15

so almost done

Answer 16

ok what next?

Answer 17

you got \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\]

Answer 18

you got the center and you know it is vertical because the bigger number is under the y term
so if \(b^2=16\) that makes \(b=4\)
vertices are 4 units above and below the center \((5,-3)\)

Answer 19

you got that ?

Answer 20

yes that help me a lot

Answer 21

also \(a^2=4\) so \(a=2\) minor axis is 2 units left and right of the center \((5,-3)\)
that also tells you the length of the minor axis 4
and the length of the major axis, from \((5,-7)\) to \((5,1)\) is 8

Answer 22

all that is left is the focus

Answer 23

you know how to find that one?

Answer 24

all the explanation is understandable so far thanks

Answer 25

um no i dont sorry

Answer 26

to find the focus, you need \(c\) which is \(c^2=b^2-a^2\)

Answer 27

in your case you have \[c^2=16-4=12\] so \[c=\sqrt{12}=2\sqrt3\]

Answer 28

starting at the center, \((5,-3)\) go up \(2\sqrt3\) and down \(2\sqrt3\)

Answer 29

which looks silly when you write it
for example one of them is \[(5,-3-2\sqrt3)\]

Answer 30

the other with a plus

Answer 31

oh one more
you need eccentricity
that is just \(\frac{c}{a}\) you have both those numbers

Answer 32

thanks so much for all ur help :)