Let P=(a,b) in the real projective plane, then what is the equation of the line passing through P and the point at infinity?
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3The real projective plane has a line at infinity, whereas the extended complex plane has a point at infinity. In your case, any line through the point $P$ will intersect the line at infinity at some point. – Christian Blatter Nov 11 '16 at 09:25
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2To explain the disparity that Christian Blatter points out, note that the real projective plane is $\mathbb R \mathbb P^2$, while the extended complex plane is $\mathbb C \mathbb P^1$. In general, for any ground field $K$, $K\mathbb P^1$ always has a single point at infinity, while $K \mathbb P^2$ has a "$K$-line" at infinity. (More precisely, $K \mathbb P^2$ has a copy of $K \mathbb P^1$ at infinity.) – Dustan Levenstein Nov 11 '16 at 09:58