Maths help please C2 circle theorems

A line, l,has equation y=mx and a circle,C, has equation x²+ y -6x -4y +9 =0
a) Given that l is a tangent to C, find the possible values of m.
b)Find the range of values of m, given that l intersects C in two distinct points
c)Find the range of values of m, given that l and C do not intersect.

please leave working out

many thanks,

keefe

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Reply 1

davros

Original post by Kexfe

Have you managed to get started on this? What have you tried so far?

Reply 2

SH0405

Here you go:

The discriminant inequality signs in parts b) and c) should be swapped.

(edited 9 years ago)

Reply 3

SH0405

Original post by Kexfe

Original post by SH0405

Here you go:

Make sure you understand my working, rather than just writing it down.

(edited 9 years ago)

Reply 4

davros

Original post by SH0405

Make sure you understand my working, rather than just writing it down.

Are you aware of the rules regarding not posting full solutions in this forum?

Reply 5

SH0405

Original post by davros

Are you aware of the rules regarding not posting full solutions in this forum?

Nope.

If I were, I wouldn't have posted a full solution.

Sorry.

Reply 6

TenOfThem

Original post by SH0405

Nope.

If I were, I wouldn't have posted a full solution.

Sorry.

Could you please delete your posts showing full solutions .. Thanks

Also .... For your own benefit .... You parts b and c are the wrong way round

(edited 9 years ago)

Reply 7

SH0405

Original post by TenOfThem

Could you please delete your posts showing full solutions .. Thanks

Also .... For your own benefit .... You parts b and c are the wrong way round

Are they? I don't think so.

(edited 9 years ago)

Reply 8

naxiv

Lovely handwriting

Original post by SH0405

Here you go:

(edited 9 years ago)

Reply 9

SH0405

Original post by naxiv

Lovely handwriting

Reply 10

TenOfThem

Original post by SH0405

Are they? I don't think so.

Yes

I take it you will not be removing your solutions

Reply 11

SH0405

Original post by TenOfThem

Yes

I take it you will not be removing your solutions

Could you explain first? Pleeeaassseeee?

(edited 9 years ago)

Reply 12

TenOfThem

Original post by SH0405

Could you explain first? Pleeeaassseeee?

Explain what

b^2-4ac >0 gives 2 solutions

(edited 9 years ago)

Reply 13

MathMeister

Original post by SH0405

...

Really lovely handwriting.

Reply 14

SH0405

Original post by TenOfThem

Explain what

b^2-4ac >0 gives 2 solutions

I didn't write that. There's an inequality sign error later on, but I'm pretty sure the parts and answers are fine.

Edit. Ah, good. My answers were correct.

(edited 9 years ago)

Reply 15

TenOfThem

Original post by SH0405

I didn't write that. There's an inequality sign error later on, but I'm pretty sure the parts and answers are fine.

I know that you didn't write that

Hence your error

Reply 16

SH0405

Original post by naxiv

Lovely handwriting

Original post by MathMeister

Really lovely handwriting.

Really? Everyone at school keeps saying that, but I didn't think it was that great. :/

Reply 17

SH0405

Original post by TenOfThem

I know that you didn't write that

Hence your error

My answers were (thankfully) still correct though.

Reply 18

TenOfThem

Original post by SH0405

My answers were (thankfully) still correct though.

No

They are wrong

Reply 19

SH0405

Original post by TenOfThem

No

They are wrong

No they're not. I know I wrote down the wrong signs, but in the lines where I go from the discriminant inequalities I jump a few stages in my head. I didn't know at the time that I had got the inequality signs wrong remember. So my final answers are correct.

The stage that I did in my head could, admittedly, have done with some written workings (well, in one sense), but it all boils down to reversing an inequality sign when one divides through by a negative. I've checked it graphically too. And after one has completed part a), it's not hard to logically deduce the answers to parts b) and c), which is why my written workings suffered, but not my answers.