If one of the lines of the pair `a x^2+2h x y+b y^2=0` bisects the angle between the positive direction of the axes. Then find the relation for `a ,b

Question

If one of the lines of the pair `a x^2+2h x y+b y^2=0` bisects the angle between the positive direction of the axes. Then find the relation for `a ,b

If one of the lines of the pair `a x^2+2h x y+b y^2=0` bisects the angle between the positive direction of the axes. Then find the relation for `a ,b ,a n dhdot`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - `a+b=-2h`
The bisector of the angle between the positive directions of the axes is `y=x`.
Since it is one of the given pair of lines
`ax^(2)+2hxy+by^(2)=0`,we have
`x^(2)(a+2h+b)=0ora+b=-2h`.

5 views Answered 2023-02-05 15:29