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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

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
the given curves are ax2+2hxy+by2+2gx=0...............(1)
anda1x2+2h1xy+b1y2+2g1x=0...............(2)
Eliminating 1stdegree terms from (1) and (2)
multiplying (1) by g1and (2) by g and subtract them we get
g1(ax2+2hxy+by2+2gx)-g(a1x2+2h1xy+b1y2+2g1x)=0
(ag1-a1g)x2+2(hg1-h1g)xy+(bg1-b1g)y2=0
These lines are mutually perpendicular if coeff of x2+coeff of y2=0
Hence we get g(a1+b1)=g1(a+b)

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