Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    A circle passes through the points A(-5,4) B(-3,-2) C(1,10).
    Find the point of intersection of the perpendicular bisectors of Ab and BC.
    Find the equation of the circle.

    I drew the diagram and found the centre is (2,3), but how can I work it out mathematically?
    Offline

    0
    ReputationRep:
    find the gradients of the lines AB and BC by doing (y2 - y1 / x2 - x1).

    then the gradient of the line that bisects that line will be found by changing the sign and putting that value over 1. e.g. if gradient is 3, perpendicular line is -1/3

    then find the mid point of each respective line. this is easy, just the mid value of both x and y co-ordinates in each case.

    then set up the equation for a straight line for both perpendicular lines: y-y1 = m(x - x1) where y1 and x1 are the values for the midpoints.

    You then have two equations and two unknowns (x and y). these solve to (2, 3) as you found out by drawing it.

    this point is also the centre of the circle. so you can work out the equation of the circle once you know the distance of this point to one of hte points given.
 
 
 
Poll
Who is your favourite TV detective?
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.