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If the equation S = represent a pair of parallel straight line , then show that ,
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Combine Equation of two parallel straight line S =
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Distance between two parallel straight line will be
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Let,
L1 and L2 are two parallel straight
So, equation will be straight line
....(1)....(2)
So ,Combination of two straight line will be
Compare Coefficient of x^2, y^2, x, y, Constant part
we find here ,
....(3).....(4)....(5)....(6)...(7)....(8)
now, we show that ,
Case (1):-
We take , by equation (5)
by equation (3) and (4) , we get there
a1 = ab1 = b
So,
Case(2):-
we take , by equation (3) and (7)
but, by equation(4) and (7) ,
Case(3):-
Distance between two parallel straight line will be
we know here ,
[ Distance between two parallel straight line ]
....(9)
Keep value by equation (6) ,
....(10)
Again, we take by equation (7) keep in (9)
we get ,
..(11)
by equation (10) and (11) ,
we find here
here three cases are proved ___________________