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If y=m 1 x and y=m 2 x be the 2 equations represented by ax 2 +2hxy+by 2 =0, then why is m 1 .m 2 =a/b

If y=m1x and y=m2x be the 2 equations represented by ax2+2hxy+by2=0, then why is m1.m2=a/b

Grade:12

2 Answers

AskiitianExpert Vinayak-iitd
8 Points
12 years ago

well the quadratic equation u posted represents a pair of lines.

So,

(y - m1x).(y - m2x) = 0  is the same as the posted quadratic...

y^2 -(m1 + m2)xy + m1m2x^2 = 0 compare this to the quadratic  ax2+2hxy+by2=0  (make coefficient of y 1 by dividing by b on both sides) =>  (a/b) x^2 + (2h/b)xy + y^2 = 0

now compare the coefficients of x

 

=> m1m2 = a/b

askiitiansexpert soumyajit_iitkanpur
8 Points
12 years ago

We have two st. line y - m1x = 0 and y - m2x =0. Therfore all the points lying on either of two st. lines will satisfy the equation (y - m1x)(y - m2x) = 0.

We acn rewrite the  equation as y2 - (m1+m2)xy + m1m2x2 =0 . .............. i)

eq. of pair of st. line is given by ax2 + 2hxy +by2 = 0 ..................  ii)

As equ i) and ii) represents the same pair of st. line so we must have,

1/b = m1m2/a = -(m1+m2)/2h

Hence m1 m2 = a/b

and m1 + m2 = - 2h/b

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