Circles question in higher maths homework

Can anyone help me answer this question, or just or the steps to do this, not too sure and hope you can understand it


The line
y +2x=k
where
k > 0 is a tangent to the circle with equation
x squared + y squared -2x -4 (circle eqn)
a) Find the value of k.
b) Deduce the coordinates of the point of contact.

If its a tangent, then the circle and the line only intersect once.

What you can hence do is form an equation that will allow you to find the coordinates of intersection in terms of k and use your knowledge of the discriminant to work out what k is.

Have a go

You're a savage dude. You're only ever on this site late at night, do you sleep?

My night is your day

That is some real vampire s h i t right there

. I meant to ask you this a long time ago, but mods kept banning me for no reason, so I had to chose the right time to resurrect myself. How did your Cambrige interview go?

Meh, one was decent, the other was horrible.

As you might know, I didn't get an offer. But idm, now I'm going to do maths and physics at Warwick and it equally excites me




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Their lost, I guess. The interviews were not formal right? So, they asked you questions relating to maths?

If its a tangent, then the circle and the line only intersect once.

What you can hence do is form an equation that will allow you to find the coordinates of intersection in terms of k and use your knowledge of the discriminant to work out what k is.

Have a go