straight lines basic

Geometry Level pending

Lines L1=ax+by+c=0 and L2=lx+my+n=0 intersect at the point P and makes an angle ϴ with each other .Find the equation of a line L different from L2 which passes through P and makes the same angle ϴ with L1.

(lx+my+n)(a²+b²)-(al+bm)(ax+by+c)=0 (lx+my+n)(a²+b²)-2(al+bm)(ax+by+c)=0 (ax+by+c)(l²+m²)-2(al+bm)(lx+my+n)=0 (ax+by+c)(l²+m²)-(al+bm)(lx+my+n)=0

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