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if one of the lines of the pair ax^2+2hxy+by^2=0 bisects the angle between +ve directions of the axes then a,b,h satif the relation :

if one of the lines of the pair ax^2+2hxy+by^2=0 bisects the angle between +ve directions of the axes then a,b,h satif the relation :

Grade:12

2 Answers

Uttam Gulshan
31 Points
11 years ago

Let the slopres of the lines be m and m'.

 Now , m+m'=-2h/b , m*m'=a/b.

Since one of the lines bisects the angle between the +ve direction of the axes this means slope of one of them is 1.

Let m=1. Therefore , m'=a/b.

=> m+m'=1+a/b.

=>-2h/b=1+a/b.

=>a+b+2h=0. Hence, the result.

HARIOM MEENA
29 Points
10 years ago

Since one of the lines bisects the angle between the +ve direction of the axes this means slope of one of them is m = 1.

let the slopes of the lines of the pair ax^2+2hxy+by^2=0 is m & m

Now , m+m=-2h/b , m*m=a/b.

> m+m=1+a/b.

> -2h/b=1+a/b.

> a+b+2h=0.

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