InterviewSolution
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InterviewSolution
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Given pair of lines `2x^(2) +5xy +2y^(2) +4x +5y +a = 0` and the line `L: bx +y +5 = 0`. ThenA. `a = 2`B. `a =- 2`C. There exists no circle which touches the pair of lines and the line L if `b = 5`.D. There exists no circle which touches the pair of lines and the line L if `b =- 5` |
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Answer» Correct Answer - A::C `2x^(2) +5xy +2y^(2) +4x 5y +a =0` represents the pair of lines if `|{:(2,5//2,2),(5//2,2,5//2),(2,5//2,a):}| =0` `rArr a = 2` So pair of lines is `2x^(2)+5xy +2y^(2) +4x +5y +2 =0` or `x +2y +1 = 0, 2x +y +2 =0` These lines are concurrent with `bx +y +5 =0` If `|{:(1,2,1),(2,1,2),(b,1,5):}| =0` `rArr b =5` Which lines are concurrent, no circle can be drawn touching all three lines. |
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