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Circle intersection question

Q. the circle x^2 + y^2 = 20 intersects the line y = x -2 at the point A and B
a) work out the coordinates of A and B
b) work out the length of AB

(I am stuck on part a :P )

Reply 1

Mr M

Study Forum Helper

Solve a pair of simultaneous equations.

Spoiler

Reply 2

rainbow.panda

For part a) I would input (x-2) into the circle equation to get x^2 + (x-2)^2 = 20 and then solve for x. Then I would just input the values of x into y = x-2 to get y :smile:

Reply 3

aking144

If you simply the equation
it will be x^2 - 2x - 9 = 0
correct ?

(edited 11 years ago)

Reply 4

joostan

Original post by aking144

If you simply the equation
it will be 2x^2 - 2x - 9 = 0
correct ?

I don't believe so. :s-smilie:

Reply 5

aking144

Original post by joostan

I don't believe so. :s-smilie:

I'm confused
could some do a trial run ?

Reply 6

joostan

Original post by aking144

I'm confused
could some do a trial run ?

Post what you did, and I will attempt to find where you're going wrong.
We're not meant to provide solutions unless it is absolutely necessary :smile:

Reply 7

aking144

Original post by joostan

Post what you did, and I will attempt to find where you're going wrong.
We're not meant to provide solutions unless it is absolutely necessary :smile:

ok

x^2 + ( x - 2 )^2 = 20
- 2x^2 - 4x + 2 = 20
- 2x^2 -4x -18
- x^2 - 2x - 9 = 0
thats what i have done so far
But the answer is an integer

Reply 8

joostan

Original post by aking144

ok

x^2 + ( x - 2 )^2 = 20
=>2x^2 - 4x + 2 = 20
=>2x^2 -4x -18
=>x^2 - 2x - 9 = 0
thats what i have done so far
But the answer is an integer

Arrows are better than - signs when saying that something implies something else. :tongue:

And what is (-2)²

Reply 9

aking144

Original post by joostan

Arrows are better than - signs when saying that something implies something else. :tongue:

And what is (-2)²

lol making all the mistakes on the net lol

Reply 10

rainbow.panda

Original post by aking144

ok

x^2 + ( x - 2 )^2 = 20
- 2x^2 - 4x + 2 = 20
- 2x^2 -4x -18
- x^2 - 2x - 9 = 0
thats what i have done so far
But the answer is an integer

You haven't multiplied it out right, it should come out like this:

x^2 + (x^2 - 4x + 4) = 20

2x^2 - 4x + 4 = 20

2x^2 - 4x - 16 = 0

You then factorise the equation to get (2x - 8)(x + 2) = 0

So 2x - 8 = 0 and x + 2 = 0

2x = 8

x = 4

Therefore x = 4 and x = -2

To find y you just put these two values of x into y = x - 2.