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

    0
    ReputationRep:
    Hi all.

    I was working through the mixed exercise for the C2 edexcel course and was wondering if I could get some help on the following question:

    Q14) The centres of the circles (x-8)^2+(y-8)^2=117
    and
    (x+1)^2 + (y-3)^2=106, are P and Q respectively.

    a) show that P lies on (x+1)^2 + (y-3)^2=106
    b) find the length of PQ

    Cheers
    Offline

    0
    ReputationRep:
    (Original post by Meha)
    Hi all.

    I was working through the mixed exercise for the C2 edexcel course and was wondering if I could get some help on the following question:

    Q14) The centres of the circles (x-8)^2+(y-8)^2=117
    and
    (x+1)^2 + (y-3)^2=106, are P and Q respectively.

    a) show that P lies on (x+1)^2 + (y-3)^2=106
    b) find the length of PQ

    Cheers
    For part a) you need to first work out the centre of the circle P which has eqn:
    (x-8)^2+(y-8)^2=117

    Once you do that plug the x and y co-ordinates into the eqn :
    (x+1)^2 + (y-3)^2=106

    if the answer is =106 then you know that point LIES on the circle. had it been <106 it would lie inside.

    for B you need to first work out the centre of the 2 circles. Then use pythagoras's theorem to work out the distance with this formula:
    • PS Helper
    Offline

    14
    PS Helper
    For (a) plug in the coordinates of P into that equation. If the LHS = the RHS then it must lie on that circle.

    For (b), notice that Q is the centre of the circle that P lies on, and so the length of PQ must be the length of the radius of the circle with centre Q.
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    For (a) plug in the coordinates of P into that equation. If the LHS = the RHS then it must lie on that circle.

    For (b), notice that Q is the centre of the circle that P lies on, and so the length of PQ must be the length of the radius of the circle with centre Q.


    Lol just noticed this :P
    Offline

    4
    ReputationRep:
    You know the x and y coords of P, so plug those into the equation and see if LHS = RHS.

    Can you remember the equation to find the distance between two points? (Think pythagoras)
    Offline

    0
    ReputationRep:
    a) show that P lies on (x+1)^2 + (y-3)^2=106
    b) find the length of PQ

    -------------
    a) Substitute the X/Y values of point P into the equation of the circle , and it should equal to 106 . If it does, it lies on it.

    b) Use the distance formula from the centre to the point.
    • PS Helper
    Offline

    14
    PS Helper
    Guyz, you definitely don't need to use Pythagoras or distance formulae to find the distance between P and Q in part (b).
    Offline

    4
    ReputationRep:
    Ah yes, if it lies on the circle the distance is simply the radius.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 3, 2011
Poll
Do I go to The Streets tomorrow night?
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.