For example, if we have a conic:$$ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$$ how should I homogenise it with a line $y=mx+c$, if my constant $c=0$? Is it possible to get a pair of straight lines by doing so?

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    $\begingroup$ What means homogenization? $\endgroup$ – Rafael Holanda Aug 18 '16 at 22:39
  • $\begingroup$ it means to make the degree of all terms in an equation same using the value of "1" from another linear equation. $\endgroup$ – Arnav Jain Aug 18 '16 at 22:42
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    $\begingroup$ Possible duplicate of What Does Homogenisation Of An Equation Actually Mean? $\endgroup$ – Rafael Holanda Aug 18 '16 at 22:44
  • $\begingroup$ I think you want to find the equation of pair of lines joining origin to the points of intersection of given line and curve? If that's the (let equation of line be $lx+my+n=0$) set $\frac{lx+my}{-n}=1$ and multiply $2gx$ and $2fy$ with $1$ and $c$ with $1^2$. $\endgroup$ – gambler101 Aug 18 '16 at 22:55

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