We have a line (in parameter):
$ x = 2\lambda $
$ y = 1-\lambda$
Find out for which values of $\lambda$ the points of the line are inside the circle of $x^2+4x+y^2-6y+5=0$
What I did:
I rewrote the circle to the form $(x+2)^2 + (y-3)^2 = 8$.
Where my problems/questions are:
First of all, I have trouble with the parameter representation of a line, how can I rewrite this to for example $y=ax+b$ or $ax+by=c$?
And there also is a problem with how to continue. I thought if replacing the $x$ and $y$ in the circle equation by $2\lambda $ and $ y = 1-\lambda$ respectively, but I get a nonsensical answer:
$(2\lambda + 2)^2 + (1-\lambda -3)^2 = 8$
$4\lambda ^2 + 4\lambda + 4 + \lambda ^2 +4\lambda + 4 = 8$
$ 5\lambda ^2 + 8\lambda =0$
$ \lambda ^2 + 1.6\lambda = 0$
And at this juncture I just quit because of the nonsensical answer I would get if continued. What am I doing wrong? What am I doing right? How does the parameter representation of a line work and how can I rewrite it into a different form?