Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    12
    ReputationRep:
    Can someone just check that I haven't fudged my way to the correct answer?

    Find in cartesian form the equation of the parabola whose focus is (3,0) and directrix is x+5=0?


    because of the focus-directrix property (0,-1) is a point on the parabola.

    x=2at now goes to (x+1)=4(t^2) and y=8t

    subbing in for y gives:

    (x+1)=4(y^2/64)
    so y^2 =16x+16
    Offline

    10
    ReputationRep:
    I can't quite follow what you've done. But here's how I'd do it:

    Suppose (x,y) is on the parabola. Then we can use the focus-directrix property:
    sqrt((x-3)^2 + y^2) = sqrt((x+5)^2 + (y-y)^2)
    x^2 - 6x + 9 + y^2 = x^2 + 10x + 25
    => y^2 = 16x + 16
    • Thread Starter
    Offline

    12
    ReputationRep:
    I can't quite follow what you've done. But here's how I'd do it
    I think its safe to say I fudged it. It didn't work with the next question. You method looks sweeter even if mine was right. Thankyou!
    Offline

    16
    ReputationRep:
    (Original post by ssmoose)
    Can someone just check that I haven't fudged my way to the correct answer?

    Find in cartesian form the equation of the parabola whose focus is (3,0) and directrix is x+5=0?


    because of the focus-directrix property (0,-1) is a point on the parabola.

    x=2at now goes to (x+1)=4(t^2) and y=8t

    subbing in for y gives:

    (x+1)=4(y^2/64)
    so y^2 =16x+16
    Hmm, could you explain what you've done?
    dvs' method is the one I use.
    • Thread Starter
    Offline

    12
    ReputationRep:
    See above, lol. I think I was away when this stuff was taught and never caught it up. Nice to see someone else going to Durham by the way Is there a P5/FP2 revision thread anywhere?
    Offline

    10
    ReputationRep:
    (Original post by ssmoose)
    Is there a P5/FP2 revision thread anywhere?
    http://www.thestudentroom.co.uk/showthread.php?t=99743
    • Thread Starter
    Offline

    12
    ReputationRep:
    it's closed. Is it possible if I ask a moderator to have it reopened?
    Offline

    16
    ReputationRep:
    (Original post by ssmoose)
    See above, lol. I think I was away when this stuff was taught and never caught it up. Nice to see someone else going to Durham by the way Is there a P5/FP2 revision thread anywhere?
    Hmm, not that I've seen.
    There might be some from last year though.
    edit: ah it's been found.
    Offline

    2
    ReputationRep:
    (Original post by ssmoose)
    it's closed. Is it possible if I ask a moderator to have it reopened?
    Yeah. Just go to the first post of the thread, for example, report it (red triangle) and in the report ask for it to be reopened.
    • Thread Starter
    Offline

    12
    ReputationRep:
    How would we go about doing the opposite then?

    For example how would we find the focus and drectrix of y^2=4x+4
    Offline

    10
    ReputationRep:
    y^2 = 4(x+1)

    Compare this to y^2 = 4ax, whose focus is at (a, 0) and directrix at x=-a. We see that a=1, so this would imply that (1, 0) and x=-1 are the focus and directrix. However we also have a translation of 1 unit to the left. So the focus and directrix actually are (0, 0) and x=-2.
    Offline

    16
    ReputationRep:
    (Original post by ssmoose)
    How would we go about doing the opposite then?

    For example how would we find the focus and drectrix of y^2=4x+4
    y^2 = 4aX = 4(x+1)
    => a = 1
    => X = x+1

    Directrix: X+a = 0 => x+1+1 = 0 => x+2=0
    Focus: X = a, y = 0 => x+1=1, y = 0 => x = 0, y = 0
    Offline

    16
    ReputationRep:
    arghh why is tsr so slow today?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 10, 2006
Poll
Are you going to a festival?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.