Higher Maths help. (Question partly done)

Hi, I would like some help with this one question please.

Question.
Find possible values of k for which the line x + y = k is a tangent to the circle
x^2 + y^2 = 2

So far I've re-arranged the x + y = k into x= k - y
I then substituted the x = k-y into the circle's equation to get (k-y)^2 + y^2 = 2
The problem is that I don't know how to get it into the form ax^2 + bx + c = 0 after multiplying the brackets out. I know to take away the two.

Reply 1

LiverpoolFC_18

I think I got it.

Is it

2y^2 - 2ky + k^2 - 2 = 0?

Then I divide by 2.

y^2 - ky + k^2/2 - 1 = 0

Is that right. What do I do next to find k?

Reply 2

soup

Use the discriminant set to 0 to find k.

Reply 3

LiverpoolFC_18

Original post by soup

Use the discriminant set to 0 to find k.

Have I done the rest right? Because k^2/2 doesn't seem right to me :confused:

Reply 4

username458263

Original post by LiverpoolFC_18

I think I got it.

Is it

2y^2 - 2ky + k^2 - 2 = 0?

Then I divide by 2.

y^2 - ky + k^2/2 - 1 = 0

Is that right. What do I do next to find k?

I wouldn't bother dividing by two, but that seems right otherwise. Set

b^2 - 4ac = 0

and solve, since there is one point of intersection where the discriminant is equal to 0.

Reply 5

Derry Rhumba

the roots must be equal so yeah just use the discriminant = 0 and then that will give you a quadratic, factorise it and that will give you 2 equal values for k

:smile: