The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Further Maths A Level Help Conics

Sort of struggling with the q link I've attached. So for part a I found S and S dash to be (2 root 5 , 0) , (- 2 root 5, 0).

For the second part I then said P = 4 root 5 + distance from P to S + distance from P to S dash but it does not seem to give a constant valiue.

I'm a bit lost and any help would be greatly appreciated. Thank you ever so much!
Below is the screenshot of the question. Thank you once again!!
Screenshot 2021-05-17 at 10.19.28.png465.1KB
Reply 2
Avatar for mqb2766
mqb2766
21
Original post by maya_jai_singh
Below is the screenshot of the question. Thank you once again!!

You realize that the construction of an ellipse is based on this property
https://www.mathwarehouse.com/ellipse/focus-of-ellipse.php#:~:text=Formula%20for%20the%20focus%20of%20an%20Ellipse&text=The%20formula%20generally%20associated%20with,center%20to%20a%20co%2Dvetex%20.

What did you try to get the two lengths of interest? Why do you not get a constant value for their sum? Sketching the ellipse with a point on the perimeter and the two lines should suggest how to approach the problem?
(edited 2 years ago)
Original post by mqb2766
You realize that the construction of an ellipse is based on this property
https://www.mathwarehouse.com/ellipse/focus-of-ellipse.php#:~:text=Formula%20for%20the%20focus%20of%20an%20Ellipse&text=The%20formula%20generally%20associated%20with,center%20to%20a%20co%2Dvetex%20.

What did you try to get the two lengths of interest? Why do you not get a constant value for their sum? Sketching the ellipse with a point on the perimeter and the two lines should suggest how to approach the problem?

Hi, thanks for your quick response. I've sent an attachment of the work I've done.
conicQuestion.jpeg180.0KB
Reply 4
Avatar for mqb2766
mqb2766
21
Original post by maya_jai_singh
Hi, thanks for your quick response. I've sent an attachment of the work I've done.

From your ellipse sketch, how is line 1 obtained?
Original post by mqb2766
From your ellipse sketch, how is line 1 obtained?

Below is the sketch of my cuve. When you say line 1, I am not too sure which line you are referring to. Once again thanks for your help.
ellipseSketch.jpeg134.9KB
Reply 6
Avatar for mqb2766
mqb2766
21
Original post by maya_jai_singh
Below is the sketch of my cuve. When you say line 1, I am not too sure which line you are referring to. Once again thanks for your help.

How do you get line 1 in your working.

Your sketch doesn't really have the x,y for P marked on it? That may help? Also drawing P "approximately vertically" above a focus may mean that you assume things about P which are not true in general. The sketch isn't wrong, but I don't see it being that useful the way it is.
(edited 2 years ago)
Original post by mqb2766
How do you get line 1 in your working.

Your sketch doesn't really have the x,y for P marked on it? That may help? Also drawing P "approximately vertically" above a focus may mean that you assume things about P which are not true in general. The sketch isn't wrong, but I don't see it being that useful the way it is.

So line 1 I basically said the perimeter is side SS dash add the other two sides. Side SS dash has length 4 root 5 and the other two sides lengths I found using Pythagoras. Hope that makes sense. I basically tried to add the length of all 3 sides but to no avail. Sorry about this.
Reply 8
Avatar for mqb2766
mqb2766
21
Original post by maya_jai_singh
So line 1 I basically said the perimeter is side SS dash add the other two sides. Side SS dash has length 4 root 5 and the other two sides lengths I found using Pythagoras. Hope that makes sense. I basically tried to add the length of all 3 sides but to no avail. Sorry about this.

Ill try for the last time, how did you find the other two side lengths using Pythagoras - how do you get line 1? Its sort of the right approach but you're not sketching or providing any working for how you calculated those values. An obvious thing to say is your line 1 "must" be wrong in that your lengths are ~x^2. x^2 is length squared, so you're not adding lengths. A sketch should make that clear.

The distance between the focii is trivial.
(edited 2 years ago)
Original post by mqb2766
Ill try for the last time, how did you find the other two side lengths using Pythagoras - how do you get line 1? Its sort of the right approach but you're not sketching or providing any working for how you calculated those values. An obvious thing to say is your line 1 "must" be wrong in that your lengths are ~x^2. x^2 is length squared, so you're not adding lengths. A sketch should make that clear.

The distance between the focii is trivial.

So below is the sketch to try to explain what I did using Pythagoras.
Thanks once again for your help but if belows sketch doesn't help, then please don't worry. I'm quite slow when it comes to maths so I'm probably just missing something key. Thank you once again for trying to deal with me :smile:
conicSketchingIII.jpeg231.5KB
Original post by maya_jai_singh
So below is the sketch to try to explain what I did using Pythagoras.
Thanks once again for your help but if belows sketch doesn't help, then please don't worry. I'm quite slow when it comes to maths so I'm probably just missing something key. Thank you once again for trying to deal with me :smile:

Your sketch still doesn't make clear what pythagoras triangles (and their lengths) you're using to find the two lengths of interest for this problem. But Im not going to ask again.

In your line 1 you are adding c^2, not c. So you need to take the square root of each of the two lengths squared, then add, then simplify to show the perimeter is constant.
(edited 2 years ago)
Original post by mqb2766
Your sketch still doesn't make clear what pythagoras triangles (and their lengths) you're using to find the two lengths of interest for this problem. But Im not going to ask again.

In your line 1 you are adding c^2, not c. So you need to take the square root of each of the two lengths squared, then add, then simplify to show the perimeter is constant.

Ah OK thanks yeah I see where I was messing up now. My bad sorry. Thanks for your time and patience nonetheless.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you