You are Here: Home >< Maths

# help Watch

1. a circle passes through A(3,1) b(8,2) C(2,6)

A) Find the point of intersection of the perpendicular bisectors of AB and BC

do I just find the mid points and gradients of AB and BC and the take the negative reciprocal of the gradient and form an equation for AB and AC using y-1=m(x-x1) and solve them simultaneously to get the points of intersection? thanks
2. yes
3. (Original post by L'Evil Fish)
yes
thanks
4. well since these are points on a circle the bisectors will be diameters, so it is asking you to find the center of the circle ?
5. (Original post by L'Evil Fish)
yes
hey fish how do I do this?

a circle touches the positive x-axis and y axes and its centre lies on the line y=3x-4

find an equation of the circle
6. (Original post by madfish)
hey fish how do I do this?

a circle touches the positive x-axis and y axes and its centre lies on the line y=3x-4

find an equation of the circle
What is the general equation of a circle?
7. (Original post by Noble.)
What is the general equation/form of a circle?
(x-a)^2+(y-b)^2=r^2
8. (Original post by madfish)
(x-a)^2+(y-b)^2=r^2
Ok, what do you know about the point . Also, how can you use the fact it touches both axes?
9. (Original post by Noble.)
Ok, what do you know about the point . Also, how can you use the fact it touches both axes?
(a,b) lies on the line y=3x -4
10. (Original post by madfish)
(a,b) lies on the line y=3x -4
Yep. Also, given that it touches the axes - what does this mean?
11. (Original post by Noble.)
Yep. Also, given that it touches the axes - what does this mean?
um, I am not too sure. :/
12. (Original post by Noble.)
Yep. Also, given that it touches the axes - what does this mean?
13. (Original post by madfish)
um, I am not too sure. :/
Well, if it touches both axes we know that there is a solution when and when .

This is much more easily visualised if you draw the line and you essentially are looking for a point on the line where you can draw a circle and have it just touch both axes - this point will be unique. However, for the equation you should be able to see there are an infinite number of solutions. For example, if the centre was and you had the radius as it would satisfy the problem, and in fact any centre of with radius works - there are infinitely many solutions. However, because this line is not going through the origin we're looking for a point on the line which is at equal distances from the y-axis and the x-axis. Again, if you don't understand this, you need to draw it. Clearly, the centre is on the line - but can we form a circle which touches both the x-axis and y-axis?
14. (Original post by Noble.)
Well, if it touches both axes we know that there is a solution when and when .

This is much more easily visualised if you draw the line and you essentially are looking for a point on the line where you can draw a circle and have it just touch both axes - this point will be unique. However, for the equation you should be able to see there are an infinite number of solutions. For example, if the centre was and you had the radius as it would satisfy the problem, and in fact any centre of with radius works - there are infinitely many solutions. However, because this line is not going through the origin we're looking for a point on the line which is at equal distances from the y-axis and the x-axis. Again, if you don't understand this, you need to draw it. Clearly, the centre is on the line - but can we form a circle which touches both the x-axis and y-axis?
okay I am so lost

how did you deduce the centre?
15. (Original post by madfish)
okay I am so lost

how did you deduce the centre?
What do you mean how do I deduce the centre? The equation of a circle:

has centre and radius

We know the centre lies on the line which implies that
16. (Original post by Noble.)
What do you mean how do I deduce the centre? The equation of a circle:

has centre and radius

We know the centre lies on the line which implies that
okay where do we go from here?:
17. (Original post by madfish)
okay I am so lost

how did you deduce the centre?
He didn't. He simply gave an example of a point that lies on the line y = 3x -4.
18. (Original post by madfish)
okay where do we go from here?:
Honestly, there's no point in me spoon feeding you all the way to the answer, it doesn't help you.

You know that the circle 'touches' the x-axis and the y-axis - do you know what this means?
19. (Original post by joostan)
He didn't. He simply gave an example of a point that lies on the line y = 3x -4.
ahh i see
20. (Original post by joostan)
He didn't. He simply gave an example of a point that lies on the line y = 3x -4.
so do you set y to 0 in the line equation to find the point the circle touches the x axis?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 28, 2013
Today on TSR

### Anxious about my Oxford offer

What should I do?

### US couple arrested - 13 children chained up

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• 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