If the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axis at concyclic points ,then prove that a1a2=b1b2 - Maths - Conic Sections

Question

If the line
a1x+b1y+c1=0
and
a2x+b2y+c2=0
cut the coordinate axis at concyclic points ,then prove that
a1a2=b1b2

Muskaan Talwar · Accepted Answer

Dear Student,

The equation of curve through intersection of lines a1x+b1y+c1=0 and a2x+b2y+c2=0 and the axes is a1x+b1y+c1a2x+b2y+c2+λxy=0Since the resultant points are concyclic,∴the curve must represent a circle⇒coefficient of x2=coefficient of y2⇒a1a2=b1b2

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If the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axis at concyclic points ,then prove that a1a2=b1b2 .

If the line a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0 cut the coordinate axis at concyclic points ,then prove that a₁a₂=b₁b₂ .