x Turn on thread page Beta
 You are Here: Home >< Maths

# C1 Circles - I need some help please watch

1. Hi There,

I really need some help with questions 13, 14 and 15 in the OCR C1&C2 textbook. It is on page 207. I really need some help as I have been struggling all day with this question.
2. (Original post by phat-chewbacca)
Hi There,

I really need some help with questions 13, 14 and 15 in the OCR C1&C2 textbook. It is on page 207. I really need some help as I have been struggling all day with this question.
What are the questions, could you write them or post a picture?
3. if you post the questions we can help you ?
4. Here you go. Thanks a lot.
Attached Images

5. 13) You need to complete the square to factorise it into a circle equation where (a,b) are the center coordinates and r is the radius.

Here, we've proved the circle's center is (r,r) and its radius is r, hence it is touching both axis!

14) Complete the square again:

From this, we know the circle is centered at (7,5). Hence, in order to lie wholly in the first quadrant (AKA the top right quarter), its radius can't be any larger than 5.

That gives you the lower bound of c. To get the higher bound, take a look at the equation for the radius squared, 74 - c. If c was at or above 74, the radius would become zero or negative, hence this is our upper bound.

15 will be similar to the above two: have a go and see if you can solve it.
6. (Original post by phat-chewbacca)
Here you go. Thanks a lot.
For 13.) Complete the square and write it in the form , then set x and y equal to 0. the centre coordinates should be the same as the radius' length.

14.) consider the center and how long the radius could be

15.) Again consider the center and the radii of each circle and show they lie outside of each other.
7. (Original post by NotNotBatman)
For 13.) Complete the square and write it in the form , then set x and y equal to 0. the centre coordinates should be the same as the radius' length.

14.) consider the center and how long the radius could be

15.) Again consider the center and the radii of each circle and show they lie outside of each other.
Again I am completed stumped. For every question I have always managed to complete the square and find the centre and radius, but I just don't understand the last part to these questions. I just don't understand the concept of considering the length of the radius. arghhh
8. (Original post by phat-chewbacca)
Again I am completed stumped. For every question I have always managed to complete the square and find the centre and radius, but I just don't understand the last part to these questions. I just don't understand the concept of considering the length of the radius. arghhh
If a circle touches both axes, it touches them at the same distance from another point. The distance from the centre to the points where the circle touches the axes are the same, this is also the radius.

Ed5 Has given a good explanation above!
9. (Original post by phat-chewbacca)
Here you go. Thanks a lot.
Question's were well explained by user's above, however for Q15 I want to add that for two circles to lie OUTSIDE each other, the sum of their radii must be less than or equal to the distance between the two centres.

Consider circle 1 with centre (a,b) and radius r:

and circle 2 with centre (c,d) with radius R:

Then circle 1 and 2 lie outside each other if, and only if:

Can you visualise this? Think of 2 arbitrary circles with a line joining their two centres. When these two circles are tangent, sum of radii equal the distance between the centres. Move one closer to the other, and then the sum is greater than the distance. Move them away and then the sum is less than the distance.
10. (Original post by RDKGames)
Question's were well explained by user's above, however for Q15 I want to add that for two circles to lie OUTSIDE each other, the sum of their radii must be less than or equal to the distance between the two centres.

Consider circle 1 with centre (a,b) and radius r:

and circle 2 with centre (c,d) with radius R:

Then circle 1 and 2 lie outside each other if, and only if:

Can you visualise this? Think of 2 arbitrary circles with a line joining their two centres. When these two circles are tangent, sum of radii equal the distance between the centres. Move one closer to the other, and then the sum is greater than the distance. Move them away and then the sum is less than the distance.
I am finding it really hard to visualise this. Do you know of any videos? Also if you don't mind could you think of all the things that I need to know for C1 Circles, and post them on here.
11. (Original post by phat-chewbacca)
I am finding it really hard to visualise this. Do you know of any videos? Also if you don't mind could you think of all the things that I need to know for C1 Circles, and post them on here.
No I do not know of any videos. It just came to me when I looked at the question and just quickly derived the conditions in a general case.

You can take a look at this I made for you. You can move the circles around by pressing on their centres and moving them. The panel on the left gives you the information you need. is the distance between the centres and is the sum of their radii. Try moving one circle closer and closer to the other and observe what happens between the two numbers.

https://www.desmos.com/calculator/6owhiberoy

Now the only thing here you may wish to imagine is that a portion of the blue line is contais the radii for both circles, from their centres to the point here the line cuts the circle; ie the circumference. I would've displayed this for you but it gets too hairy on desmos with generality.

Turn on thread page Beta
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: September 17, 2016
Today on TSR

### Happy St Patrick's day!

How are you celebrating?

### Stay at sixth form or go to college?

Discussions on TSR

• Latest
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

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