InterviewSolution
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InterviewSolution
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If graph of `xy = 1` is reflected in `y = 2x` to give the graph `12x^(2) +rxy +sy^(2) +t = 0`, thenA. `r = 7`B. `s =- 12`C. `t = 25`D. `r +s =- 19` |
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Answer» Correct Answer - B::C::D Let image of point `A(alpha,beta)` about `y = 2x` is `B (a,b)` `rArr` mid point of AB i.e. `M -= ((alpha +a)/(2),(beta+b)/(2))` lie on `y -2x =0` `rArr ((beta +b)/(2)) =2 ((alpha +a)/(2)) rArr beta +b = 2alpha +2a `(i) and slope of `AB =- (1)/(2)` `rArr (beta-b)/(alpha-a) = -(1)/(2) rArr beta -b =- (1)/(2) alpha +(a)/(2)` (ii) Subtracting (i) and (ii), `rArr 2b = (5)/(2) alpha +(3)/(2) alpha rArr a = (4b-3a)/(5)` `rArr beta =(8b -6a)/(5) +2a - b = (3b+4a)/(5)` `rArr (alpha, beta)` lies on `xy =1` `rArr ((4b-3a)/(5))((3b+4a)/(5)) =1` `rArr 12b^(2) +7ab -12 a^(2) =25` `rArr 12 x^(2) - 7xy =12y^(2) +25 =0` |
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