InterviewSolution
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InterviewSolution
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The combined equation of the pair of lines through the origin and perpendicular to the pair of lines given by `ax^(2)+2hxy+by^(2)=0`, isA. `ax^(2)-2hxy+by^(2)=0`B. `bx^(2)+2hxy+ay^(2)=0`C. `bx^(2)-2hxy+ay^(2)=0`D. `bx^(2)+2hxy-ay^(2)=0` |
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Answer» Correct Answer - C Let `y=m_(1)x and y=m_(2)x` be the lines represented by `ax^(2)+2hxy+by^(2)=0`. Then, `m_(1)+m_(2)=-(2h)/(b) and m_(1)m_(2)=(a)/(b)" …(i)"` The equation of the lines passing through the origin and perpendicular to `y=m_(1)x and y=m_(2)x` respectively are `m_(1)y+x=0 and m_(2)y+x=0` The combined equation of these lines is `(m_(1)y+x)(x_(2)y+x)=0` `rArr" "m_(1)m_(2)y^(2)+xy(m_(1)+m_(2))+x^(2)=0` `rArr" "(a)/(b)y^(2)-(2h)/(b)xy+x^(2)=0` `rArr" "ay^(2)-2hxy+bx^(2)=0` NOTE- The equation of the pair of lines through the origin and perpendicular to the pair of lines given by `ax^(2)+2hxy+by^(2)=0` can be obtained by interchanging the coefficients of `x^(2)` and `y^(2)` and changing the sign of the term containing xy. |
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