Q. IF a+2hxy+b+2gx+2fy+c=0 represents a pair of parallel straight lines, then:-

a)hf=bg  b)a=b  c)=bc

the answer is a) but how?

it can in no situation be a)

a) is incorrect

all options are wrong answer is h^2=ab if lines parallel then homogenous part of equation shud be perfect square

are what has happened to everyone it is a standard result that if two lines are parallel then h^2=ab

is the condition that a homegenous second degree equation of straight lines PASSING THROUGH THE ORIGIN must satisfy if the two lines are parallel. Such an equation is of the form 

In the question, we have been given the general equation of second degree : which represents a pair of straight lines if  and only if = 0

and



SOLUTION:

In this particular question, it is given that the two lines are parallel.

Let the equations of the two lines be and

The joint equation of the two lines is given by  

 

Comparing with (1),  

From the above we can see that

. Similarly, we can see that is also correct. So the given answers are correct.

Answer :