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# If slope of one of the lines represented by ax²+2hxy+by²=0 is n times the other, then

Vikas TU
14149 Points
one year ago
Dear student
Here, concept of second degree equations is applied.
y1=m1x and y2=m2x are the two lines of the general second degree

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2075 Points
one year ago
vikas’ answer is wrong and unsatisfactory.
given ax²+2hxy+by²=0 , we can divide the entire eqn by x^2 and note that y/x= m (slope) since clearly ax²+2hxy+by²=0 passes through (0,0)
so we get a+2hm+bm^2=0 or bm^2+2hm+a=0. this is a quad in m. it has two roots m1 and m2. but given that m2= n*m1
so m1+m2= – 2h/b= m1(1+n)....(1)
similarly m1*m2= a/b= n*(m1)^2.....(2)
from (1) and (2) eliminate m1 and you will obtain the reqd relation.
kindly approve :)