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Equation of tangent to circle- HELP URGENTLY NEEDED

The line with equation mx-y-2=0 touches the circle with equation x^2+6x+y^2-8y=4. Find 2 possible values of m, giving your answers in exact form.

I've attempted everything, but I can't seem to do it.

I found the centre of the circle and found the gradient of the circle to be -2, making the gradient of the tangent 0.5.

I'm so confused, can someone please explain how to get the answers?

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Reply 1

EmilySarah00

Original post by bananabrainedbee

Hey! Sorry you haven't had a response yet.

Could you post your full working I can help you from what you've already done?

Reply 2

CompSci in2k17

Find a coordinate at the radius of the circle then use the equation y-y1 = 0.5(x-x1) to get the equation of the line

Reply 3

username2975726

1) Write mx-y-2=0 in the form y=mx+c
2) work out equation of circle
3) Subsitute y=mx-2 into the y in the equation of the circle
4) Expand and simplify
5) factor out x so in brackets you get m and numbers only
6) work out discriminant (b^2-4ac)
7) sub into m

Reply 4

number0

I remember doing this question in one of those end of chapter tests, you need to remember how the discriminant is equal to zero when they only touch

Reply 5

Rolls_Reus_0wner

Original post by bananabrainedbee

Where have you got this question from?

Reply 6

number0

Original post by Rolls_Reus_0wner

Where have you got this question from?

It is from one of the Edexel new spec maths end of chapter tests. i think only teachers are able to get them.

Reply 7

Rolls_Reus_0wner

Original post by number0

It is from one of the Edexel new spec maths end of chapter tests. i think only teachers are able to get them.

makes sense cause that came up in my mock. Was proper hard. Need to know where the school gets such hard questions

Reply 8

number0

Original post by Rolls_Reus_0wner

makes sense cause that came up in my mock. Was proper hard. Need to know where the school gets such hard questions

Yeh, defo set by the exam board. To be fair some textbook questions can be quite difficult

Reply 9

username2975726

Original post by Rolls_Reus_0wner

Where have you got this question from?

theyre in the as maths textbook

Which one?

Original post by Rolls_Reus_0wner

Which one?

https://www.amazon.co.uk/Edexcel-level-Mathematics-Textbook-Further/dp/129218339X

What page

jheez is that you yeah

Reply 14

username2975726

Original post by thotproduct

jheez is that you yeah

im out here on that as maths tingg

Reply 15

number0

Think there are similar questions in the textbook but this one specifically was in one of the tests I think

Reply 16

kateroseco

Would you be able to tell me what you mean by work out the equation of the circle?? Im not sure what to do with it thanks

Reply 17

username2975726

Original post by kateroseco

Would you be able to tell me what you mean by work out the equation of the circle?? Im not sure what to do with it thanks

you need to complete the square of the given equation of the square for x and y respectively so the equation of the circle is in the form (x-a)^2 + (y-b)^2 = r^2.

Actually, you don't have to do that. You can simply sub y=mx-2 into the equation of the given circle if you want without putting it in correct circle form . step 1 isn't needed for this question.

Reply 18

kateroseco

okay so i got:

x^2(1+m^2) + x(6-12m) + 16 = 0

and im not sure which bits to use for the b^2-4ac.... thank you for your help

Reply 19

username2975726

Original post by kateroseco

okay so i got:

x^2(1+m^2) + x(6-12m) + 16 = 0

and im not sure which bits to use for the b^2-4ac.... thank you for your help

Then parts inside the bracket, as you are solving to find m, the unknown. Thats why you took out x, to be able to solve for m.

So you know the discriminant is 0 as the lines touch the circle

(6-12m)^2 - (4)(1+m^2)(16)=0