Question

Find the center, vertices, and foci of the ellipse with equation 4x2 + 6y2 = 24. @rajee_sam @jim_thompson5910

Answer 1

if you rewrite it in std. form you will have

x²/6 + y²/4 = 1

Answer 2

now my center is (h,k) which is (0,0)

a² = 6 , a = √6
b² = 4 , b = 2

for ellipse

a² - c² = b²
c² = a² - b² = 6-4 = 2
c = √2

Vertices : ( h± a , k) , ( 0 + √6 , 0) and (0-√6 , 0)
(√6, 0) and ( -√6 , 0)

Foci : ( h ± c , k), ( 0 + √2 , 0) and ( 0-√2 , 0)
(√2,0) and (-√2 , 0)

Answer 3

those aren't any of my answer choices? @rajee_sam

Answer 4

what are your choices?

Answer 5

oh wait nevermind my bad it is

Answer 6

could you help with one more? you're a lifesaver dude thanks so much! @rajee_sam

Answer 7

I am not dude

Answer 8

But I 'll help you never the less

Answer 9

Are you understanding how to do it?

Answer 10

Eliminate the parameter. x =1/2t, y = 3t^3 - 1
Oh my gosh i'm so sorry!

Answer 11

i think it's y = 24x^3 - 1 but i'm not 100% sure

Answer 12

for eliminating parameters you have to eliminate the t and express y in terms of x.

for that you have to find what t is in terms of x. So use x = 1/2t and solve for t.

Can you tell me what t is from x = 1/2t?

Answer 13

so i'm guessing y = 24x^3 - 1 is not the right answer?

Answer 14

no

Answer 15

i'm stuck. I have no idea what you mean

Answer 16

you are given 2 equations

x = 1/2t ----(Equation 1)

and

y = 3t³ -1 ----(equation 2)

Answer 17

In equation 1 you have x on one side and t on the other side

Answer 18

you have to solve for t meaning you have to rewrite this equation as

t = "something"

Can you do that?

Answer 19

t = 2?

Answer 20

\[x = \frac{ 1 }{ 2t }\]

If I rearrange the x and t from this equation I get ,

t = 1/2x

Answer 21

Now I know what t is in terms of x

Answer 22

put this in place of t in equation no. 2

Answer 23

\[y = 3 (\frac{ 1 }{ 2x })^{3} - 1\]

Answer 24

\[y = 3(\frac{ 1 }{ 8x ^{3} }) - 1\]\[y = \frac{ 3 }{ 8x ^{3} } - 1\]

Now I have eliminated the parameter

Answer 25

@hfskibo

Answer 26

ohh ok that makes so much sense. Thanks! can you hellp with another one?

Answer 27

last one I have to go after that

Answer 28

ok thank you so much!

Answer 29

I hope you are learning in the process and not just getting answers out of me

Answer 30

I would suggest you try similar problems without help and familiarize yourselves with the conic sections.

Answer 31

Find the rectangular coordinates of the point with the polar coordinates.

Answer 32

I am learning! you're doing a great job of explaining & i understand all these so much better now! thank you!

Answer 33

@rajee_sam

Answer 34

Ok

Answer 35

You are given a polar coordinate which is ( r, Θ) ---> ( 3, 2π/3)

r = 3 and Θ = 2π/3 = 120°

Now rectangular coordinates are written as (x,y) your usual point coordinates.

now this is calculated as follows using your polar coordinates

x = r cos Θ

y = r sin Θ

you know r and Θ, so find your x and y and write your coordinates.

Answer 36

Can you find the coordinates?

Answer 37

-3,2?