Question

Need some help with Ellipses if anyone can help pls. Will fan n medal.

36x^2 + 49y^2 = 1,764
The foci are located at:
(-√13, 0) and (√13,0)
(0, -√13) and (0,√13)
(-1, 0) and (1, 0)

Answer 1

The simplest form of the equation for an ellipse centere3d at the origin is\[\frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2 }=1\]

Answer 2

Your job is to put \[36x^2+49y^2=1764 \]

Answer 3

...into that form. What would you do first?

Answer 4

36 is a and 49 is b right?

Answer 5

No. 36 = a^2; 49 = b^2. what are a and b?

Answer 6

yea thats what i meant

Answer 7

Again: What are a and b?

Answer 8

a^2 and b^2

Answer 9

No.
a^2 = 36. What is a?
b^2=49. What is b?

Answer 10

a=1296
b=2401

Answer 11

try squaring 1296. Is the answer 36?
If not, something's wrong. Check your own work.

Answer 12

yea
36*36=1296
49*49=2401

Answer 13

Please re-read my first two posts.

Answer 14

...especially the "Your job is to ... " one.

Please divide all 3 terms by 1764.

Your results?

Answer 15

3 terms?

Answer 16

Look at my second post, at the very top of this conversation. There are 3 terms in that equation.

Divide each by 1764, please.

Answer 17

do i square them first?

Answer 18

49 + 36=1

Answer 19

No. That's where you are having problems.
Ask yourself this question: "Why do I believe I should square 36 and / o r 1764.

Answer 20

Please take my instructions at face value. Look at my 2nd post, at the top of this conversation, and divide each term by 1764.

Type in your results, below.

Note that 36 + 49 does not come out to 1.

Answer 21

i did.....
1764/36=49
1764/49=36
1764/1764=1

Answer 22

1764/85=20.75..........idk

Answer 23

\[\frac{ 36x^2 }{ 1764 }+ \frac{ 49y^2 }{ 1764 }=\frac{ 1764 }{ 1764 }\]

Answer 24

There is no reason to divide 1764 by 85.

Look at my most recent post. I'm asking you to simplify it.

Write your result as an equation.

Answer 25

To simplify 36x^2 / 1764, divide 36 into 1764. Write your result as\[\frac{ x^2 }{ a^2 }\] where a^2 =1764/49

Answer 26

Excuse me, that was supposed to be "where a^2=1764/36."

Answer 27

i dont get it.....................

Answer 28

36/1764 i got 0.2......

Answer 29

1764/36 i got 49

Answer 30

Have you worked with equations of elllipses before?

You are given 36x^2 + 49y^2 = 1764.

This has to be re-written as an equation in standard form for an ellipse, which is \[\frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2 }=1.\]

Answer 31

nope have not worked on these before, and my teacher is out sick thats y im using this

Answer 32

Yes, your 49 is correct, so your equation is now beginning to look as it should:

Answer 33

49/1764?

Answer 34

\[\frac{ 36x^2 }{ 1764 }+\frac{ 49y^2 }{ 1764 }=\frac{ 1764 }{ 1764 }\]

Answer 35

The first term becomes\[\frac{ x^2 }{ 49 }\] and the third term becomes just 1.

Answer 36

What is the 2nd term?

Answer 37

x^2/36

Answer 38

Yes, so now you have \[\frac{ x^2 }{ 7^2 }+\frac{ y^2 }{ 6^2 }=1\]

Answer 39

Note: 49 = 7^2, and 36 = 6^2.

Answer 40

yup

Answer 41

Now we have to identify 2 values: those for a and b. We'll need to calculate c.

I ask you to look up http://www.purplemath.com/modules/ellipse.htm

and to at least skim it.

For now, take my word for it, that a = 7 and b = 6. Refer to my last equation to see where the 7 and 6 come from.

Answer 42

According to http://www.purplemath.com/modules/ellipse.htm

b^2 + c^2 = a^2.
Since b=6 and a=7,

this works out to (6)^2 + c^2 = (7)^2.

Answer 43

Alternatively, 36 + c^2 = 49
...which means that c^2 must equal what?

Answer 44

13?

Answer 45

Yes. If c^2=13, what is c? Do NOT square; instead, take the square root of both sides.

Answer 46

7+6

Answer 47

or 6+7

Answer 48

sqrt 36 is 6. sqrt 49 is 7. 6+7=13

Answer 49

sqrt(36)=6, yes. 36 is a perfect square, so this is easy.
sqrt(49)=7, yes. 49 is also a perfect square.
sqrt(13) = sqrt(13) 13 is not a perfect square, so the "square root of 13" is sqrt(13). Can't simplify that.

Answer 50

Write a summary now.
a=
b=
c=

Answer 51

a=49
b=36
c=13

Answer 52

or
a=7
b=6
c=13

Answer 53

Check that "c" please. Review our discussion. c is not equal to 13.

Answer 54

3.60555127546..........

Answer 55

3.6

Answer 56

As before, please leave the "square root of 13" as a radical: