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If one of the lines given by the equatio...

If one of the lines given by the equation `a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0` coincides with one of the lines given by `a_(2)x^(2)+2h_(2)xy+b_(2)y^(2)=0` and the other lines represented by them are perpendecular then prove that.
`h_(1)((1)/(a_(1))-(1)/(b_(1)))=h_(2)((1)/(a_(2))-(1)/(b_(2)))`

Answer

Step by step text solution for If one of the lines given by the equation a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 coincides with one of the lines given by a_(2)x^(2)+2h_(2)xy+b_(2)y^(2)=0 and the other lines represented by them are perpendecular then prove that. h_(1)((1)/(a_(1))-(1)/(b_(1)))=h_(2)((1)/(a_(2))-(1)/(b_(2))) by MATHS experts to help you in doubts & scoring excellent marks in Class 11 exams.

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If the pair of lines a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 and a_(2)x^(2)+2h_(2)xy+b_(3)y^(2)=0 have one line in common then show that (a_(1)b_(2)-a_(2)b_(1))^(2)+4(a_(1)h_(2)-a_(2)h_(1))(b_(1)h_(2)-b_(2)h_(1))=0

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Knowledge Check

  • If the slopes of the lines represented by 6x^(2)+2hxy+y^(2)=0 are in the ratio 1:2 then h=

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    `(ab' -a'b)^2 =4(ha'-h'a)(bh'b'h)`
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