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If the lines joining origin and point of intersection of curves ax 2 +2hxy+by 2 +2gx=0 and a1x 2 +2h1xy+b1y 2 +2g1x=0 are mutually perpendicular,then prove that- g(a1+b1)=g1(a+b)

If the lines joining origin and point of intersection of curves ax2+2hxy+by2+2gx=0 and a1x2+2h1xy+b1y2+2g1x=0 are mutually perpendicular,then prove that-
g(a1+b1)=g1(a+b)

Grade:12

1 Answers

Agniva Kolay
35 Points
6 years ago
a petty question on homogenization of equation.
ax2+2hxy+by2+2gx(1)=0 ...1 a1x2+2h1xy+b1y2= -2g1x ...2
a1x2+2h1xy+b1y2/(-2g1x)=1 ...3
now replacing 1 in eq 1 by a1x2+2h1xy+b1y2/(-2g1x)
we get a eqtn of pair of st lines passing through origin.
since angle betwn line is given 90 degree
so coeff of x^2 + coeff of y^2=0
so we getg(a1+b1)=g1(a+b) proved :D
 

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