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How do we make a combined equation of a curve $$ax^2+2hxy+by^2+2gx+2fy+c=0$$ and line $$lx + my = n?$$

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2 Answers 2

$$(ax^2+2hxy+by^2+2gx+2fy+c)\cdot(lx+my-n)=0$$

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But by Mutiplying both the equations we can't find the point of intersection of the curves and the line.. –  Ravi Jan 16 '13 at 18:03
    
But it is an equation that describes the combination (set-theoretic union) of the curve and the line. The question said nothing about finding the intersection points. –  Hagen von Eitzen Jan 16 '13 at 18:08
    
Sorry, my mistake. Actually we have to develop a combined equation of line passing through origin and intersection point of the curve and the line. –  Ravi Jan 16 '13 at 18:14

In assumption that $l^2+m^2\ne{0}$ is possible to solve the linear equation $lx+my=n$ with respect to one of variables, say $x: \;\;x=\dfrac{n-my}{l}$ and substitute it into the first equation

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We have to apply concept of homogenousation here? –  Ravi Jan 16 '13 at 18:12
    
You want apply homogenization to ...? –  M. Strochyk Jan 16 '13 at 18:39

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