Year 12s: what will be the first way you research your future options? >>

c2 circles

Scroll to see replies

Reply 20

TenOfThem

Original post by lolman42

subbing the equation of the line into the circle I get

7x^2 + 60x + 90 = 0

what do I do from here? :smile:

You must have realised that was wrong when you could not do part (a)

Reply 21

TenOfThem

Original post by Indeterminate

Surely, as it's saying "write down", it's asking for

y=\sqrt{10}

I think you have mis-read or mis-understood the question

Reply 22

lolman42

Original post by TenOfThem

You must have realised that was wrong when you could not do part (a)

okay i am not too sure now

is the expansion 10x^2 + 60x + 100 = 10 ?

i did b^2-4ac but it does not equal
0

FORGET ALL WHAT i WROTE THERE!! i HAVE GOT IT NOW. what do I do for b now?

Reply 23

TenOfThem

Original post by lolman42

okay i am not too sure now

is the expansion 10x^2 + 60x + 100 = 10 ?

i did b^2-4ac but it does not equal
0

FORGET ALL WHAT i WROTE THERE!! i HAVE GOT IT NOW. what do I do for b now?

So

You know know the point rom (a) so, sketch and use symmetry

Reply 24

lolman42

Original post by TenOfThem

So

You know know the point rom (a) so, sketch and use symmetry

I still do not now the point

do I solve 10x^2 + 60x +90 =0 to find it?

Reply 25

TenOfThem

Original post by lolman42

I still do not now the point

do I solve 10x^2 + 60x +90 =0 to find it?

yes

I suggest that you divide by 10 and use the fact that there is only one solution to spot the obvious factorisation

Reply 26

lolman42

Original post by TenOfThem

yes

I suggest that you divide by 10 and use the fact that there is only one solution to spot the obvious factorisation

okay so x= -3

Reply 27

TenOfThem

Original post by lolman42

okay so x= -3

Sketch and symmetry

Reply 28

dragonkeeper999

TenOfThem's method is basically to find the intersection of the two curves, and show that there is only one intersection, so the line must be a tangent to the circle (think, if it crossed the circle there would have to be two solutions, one where it goes into the circle and one where it exits it).

Reply 29

lolman42

Original post by TenOfThem

Sketch and symmetry

sorry, I am going to have to sound really silly here.

But I am lost :frown:

Reply 30

TenOfThem

Original post by lolman42

sorry, I am going to have to sound really silly here.

But I am lost :frown:

Have you sketched?

Reply 31

lolman42

Original post by TenOfThem

Have you sketched?

I am not exactly sure what I am meant to be sketching

Reply 32

TenOfThem

Original post by lolman42

I am not exactly sure what I am meant to be sketching

A circle

x^2 + y^2 = 10

and a line

y = 3x + 10

Reply 33

lolman42

Original post by TenOfThem

A circle

x^2 + y^2 = 10

and a line

y = 3x + 10

yep, I already had that drawn :smile:

Reply 34

TenOfThem

Original post by lolman42

yep, I already had that drawn :smile:

So you have a circle

Then you have a line from (0,10) down to (-3,1)

As I say, symmetry will show you the other line

Reply 35

lolman42

Original post by TenOfThem

So you have a circle

Then you have a line from (0,10) down to (-3,1)

As I say, symmetry will show you the other line

I can't see the symmetry..

Reply 36

lolman42

Original post by TenOfThem

So you have a circle

Then you have a line from (0,10) down to (-3,1)

As I say, symmetry will show you the other line

surely there can only be one line passing through 0,10?

Reply 37

TenOfThem

Original post by lolman42

surely there can only be one line passing through 0,10?

Well, infinite lines will pass through (0,10)

But there are 2 that pass through there and are tangents to the circle

I cannot work out why you cannot see it