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Can you tell me how to get combined equation from two lines passing through the same point?

Can you tell me how to get combined equation from two lines passing through the same point?

Grade:

2 Answers

abhishek jaiswal
16 Points
9 years ago

L1 : equation of line 1 : ax +by +c=0

L2 : equation of line 2 : px +qy +r=0

Required equation (L3):L1 + (lambda)*L2   where lambda is a constant  

Lets say lambda =  H(constant) dont know how to make lambda  .

Then the eqution is :  (a+ H*p)x+(b+H*q)y+(c+H*r)=0

to get the value of H(lambda) the point given satisfies all the 3 equations L1,L2 and L3 ,put the point in L3 to get value of lambda

Hope this helps

abhishek jaiswal
16 Points
9 years ago

sorry it was my first reply to an answer so made a bit of mistake

the correct equation is L3:- L1+(lambda)*L2=0

this is the general equation of a line passing through the point of intersecti

Different values of lambda give different lines 

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