Removal of First Degree Terms
Category : JEE Main & Advanced
Let point of intersection of lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] .....(i) is \[(\alpha ,\beta )\].
Here \[(\alpha ,\beta )=\left( \frac{bg-fh}{{{h}^{2}}-ab},\frac{af-gh}{{{h}^{2}}-ab} \right)\]
For removal of first degree terms, shift the origin to \[(\alpha ,\beta )\] i.e., replacing \[x\] by \[(X+\alpha )\]and \[y\] be \[(Y+\beta )\]in (i).
Alternative Method : Direct equation after removal of first degree terms is \[a{{X}^{2}}+2hXY+b{{Y}^{2}}+(g\alpha +f\beta +c)=0\],
where \[\alpha =\frac{bg-fh}{{{h}^{2}}-ab}\] and \[\beta =\frac{af-gh}{{{h}^{2}}-ab}\].
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