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

# C2 coordinate geometry watch

1. A bit confused about these:

9) The line y=2x-2 meets the circle (x-2)²+(y-2)²=20 at A and B.
a) Find the coordinates of A and B. ---> Done that (0,-2), (4,6).
b) Show that AB is a diameter of the circle. (How would you prove this?)

10) The line x+y=a meets the circle (x-p)²+(y-6)²=20 at (3,10), where a and p are constants.
a) Work out the value of a.
b) Work out the two possible values of p.
2. 9. b) The radius of the circle is √20- agreed?
So the diameter would be 2√20 = 4√5

The length AB = √ [(4-0)²+(6+2)²] = √(16+64) = √80 = √16.√5 = 4√5

The length AB is equal to the length of the diameter, hence AB is a diameter of the circle.
3. Ohh, thank you! Actually, I have one more...

1) The line y=2x-8 meets the coordinate axes at A and B. The line AB is a diameter of the circle. Find the equation of the circle.
4. 10. a) If the line with equation x+y = a passes through the point (3,10), then:

3+10 = a
a = 13

b) (x-p)²+(y-6)²=20

The circle must go through (3,10)

=> (3-p)² + (10-6)² = 20

9 - 6p + p² + 16 = 20

p² - 6p + 5 = 0

(p-1)(p-5) = 0

p = 1 or p = 5
5. (Original post by *girlie*)
1) The line y=2x-8 meets the coordinate axes at A and B. The line AB is a diameter of the circle. Find the equation of the circle.
x = 0, y = -8
=> A(0,-8)

y = 0, x = 4
=> B(4,0)

If AB is the diameter, the midpoint of AB will be the centre (C)

C(2,-4)

Length AB = √(4²+8²) = √80 = 4√5
The radius will be half the length of the diameter
=> r = 2√5

Eq of circle is in the form (x-a)² + (y-b)² = r² , where C(a,b)

=> (x-2)² + (y+4)² = 20
6. Thanks, mockel!

Turn on thread page Beta

### Related university courses

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: June 18, 2005
The home of Results and Clearing

### 2,827

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Sheffield Hallam University
Tue, 21 Aug '18
2. Bournemouth University
Clearing Open Day Undergraduate
Wed, 22 Aug '18
3. University of Buckingham
Thu, 23 Aug '18
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

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