InterviewSolution
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InterviewSolution
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The image of the pair of lines respresented by `ax^2 + 2hxy + by^2 = 0` by the line mirror `y = 0` is:(A) `ax^2-2hxy+by^2=0`(b) `bx^2-2hxy+ay^2=0`(c) `bx^2+2hxy+ay^2=0`(d) `ax^2-2hxy-by^2=0`A. `ax^(2)-2hxy+by^(2)=0`B. `bx^(2)+2hxy+ay^(2)=0`C. `bx^(2)-2hxy+ay^(2)=0`D. none of these |
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Answer» Correct Answer - A Let `y=m_(1) x, 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)` Clearly, if `y=m_(1)x` makes an angle `theta_(1)` with y = 0 (x-axis), then its image in line mirror y - 0 makes an angle `-0_(1)` with x-axis. So, its equation is `y=tan(-theta_(1))x or y=-(tan theta_(1))x or y=-x_(1)x`. Similarly, equation of the image of `y-m_(2) x` in `y-0` is `y=-m_(2)x` Therefore, the combined equation of the images is `(y+x_(1)x)(y+m_(2)x)=0` `rArr" "y^(2)+xy(m_(1)+m_(2))+m_(1)m_(2)x^(2)=0` `rArr" "y^(2)-(2h)/(b)xy+(a)/(b)x^(2)=0" [Using (i) ]"` `by^(2)-2hxy+ax^(2)=0` |
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