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Question

If the lines a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinates axes in concyclic points, then
 



A

a1b1=a2b2
 

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B

a1a2=b1b2
 

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C

a1+a2=b1+b2
 

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D

a1a2=b1b2

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Solution

The correct option is D

a1a2=b1b2


Let the given lines be L1a1x+b1y+c1=0 and L2a2x+b2y+c2=0. Suppose L1 meets the coordinate axes at A and B and L2 meets at C and D. Then coordinates of A, B, C, D are
A(c1a1,0),B(0,c1b1)C(c2a2,0), and D(0,c2b2)
Since A, B, C, D are concyclic, therefore OA.OC=OD.OB

(c1a1)(c2a2)=(c2b2)(c1b1)a1a2=b1b2 


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