ellipse

Kiran · 2006-12-07 11:34:13

consider the ellipse that has vertices at (0,5) ,(0,-5) and foci at (0,3) and (0,-3)
and write its equation in standard form.

gnitsuk · 2006-12-07 22:13:47

The standard equation of an ellipse is:

Where a is half the length of the semi-major axis and b is half the length of the semi-minor axis.

So all we have to do is determine the values of a and b.

So in this case:

This is because your semi-major axis is of length 10 - the distance between (0,-5) and (0,5).

Also, the foci of the ellipse given in standard form are at:

Where e is the eccentricity of the ellipse and for an ellipse e < 1

So we have in this case that

And finally, in the equation of standard form

So finally we have the value of a and b in the equation. So our answer is:

As a check, note that the points (-5,0) and (5,0) are indeed on the curve.

Last edited by gnitsuk (2006-12-08 02:38:01)

soha · 2006-12-07 22:15:22

i did nt understand anything
what are u talking about

LQ · 2006-12-08 00:21:50

Some cool stuff. Maxed.

soha · 2006-12-09 01:01:14

what is maxed

LQ · 2006-12-09 01:09:46

All I have to do is remember how I get a. Then I can get the whole equation.

That is maxed. I think.

mathsyperson · 2006-12-09 01:38:50

That's correct for a standard ellipse, but soha's ellipse is longer along the y axis rather than the x axis.

So the equation of soha's ellipse would be y²/5² + x²/4² = 1.

soha · 2006-12-09 04:09:18

meaning of ellipse=?

mathsyperson · 2006-12-09 11:15:30

You can define an ellipse with two points and a length. If your defining points are A and B and your length is l, then your ellipse is the locus of all points X that meet the condition that AX+BX = l.

gnitsuk · 2006-12-11 00:21:16

Cool. Quiet right. I simply read (0,3) and (0,-3) as (3,0) and (-3,0) and carried on regardless!

As an alternative definition. You can understand an ellipse as follows:

Stick two pins in a piece of paper and join them together with a length of string (make sure the string has some slack in it). The using a pen, pull the string taught and then keeping the string taught move the pen wherever it will go (keep that string taught) this will draw an ellipse. The sum of the distances of the pen from each pin is always the same.

http://chickscope.beckman.uiuc.edu/expl … /pins.html

If the two pins are pinned in the same position you get a circle. So a circle is a special case of an ellipse.

In the case of your ellipse, the distance between the pins would be 6 (one above the other as your ellipse lies with its major axis along the y-axis) and the length of the string 10.

Last edited by gnitsuk (2006-12-11 00:29:09)

yo mama · 2006-12-11 05:45:30

ill live ur love if u no wit i mean

Mandy Mayday · 2006-12-12 00:29:47

Hi guys!!!
Interesting what you can do. When I lived in Krakow, Poland, an old city with tradition, I knew a man who could do the same stuff like you within the blink of an eye. Ellipsis? I'll calcultate it for ya°!

Kiran · 2006-12-12 09:11:23

yo mama wrote:

ill live ur love if u no wit i mean

what do you mean by this????

John E. Franklin · 2006-12-12 09:49:19

I think what yo mama means is that he has ESP and he will live the love we have by experiencing it for himself. Just a thought.

Math Is Fun Forum

#1 2006-12-07 11:34:13

ellipse

#2 2006-12-07 22:13:47

Re: ellipse

#3 2006-12-07 22:15:22

Re: ellipse

#4 2006-12-08 00:21:50

Re: ellipse

#5 2006-12-09 01:01:14

Re: ellipse

#6 2006-12-09 01:09:46

Re: ellipse

#7 2006-12-09 01:38:50

Re: ellipse

#8 2006-12-09 04:09:18

Re: ellipse

#9 2006-12-09 11:15:30

Re: ellipse

#10 2006-12-11 00:21:16

Re: ellipse

#11 2006-12-11 05:45:30

Re: ellipse

#12 2006-12-12 00:29:47

Re: ellipse

#13 2006-12-12 09:11:23

Re: ellipse

#14 2006-12-12 09:49:19

Re: ellipse

Board footer