InterviewSolution
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InterviewSolution
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The differential equation of the family of straight lines whose slope is equal to y - intercept ,isA. `a(d^(2)y)/(dx^(2))+((dy)/(dx))^(3)=0`B. ` 2a (d^(2)y)/(dx^(2))+((dy)/(dx))^(3)=0`C. ` 2a (d^(2)y)/(dx^(2))- ((dy)/(dx))^(3)`D. ` a (d^(2)y)/(dx^(2))-((dy)/(dx))^(3)=0` |
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Answer» Correct Answer - b Equation of the family of such parabola is ` ( y - k)^(2) = 4a (x-h) " "` …(i) where h and k are arbitrary constants ltbRgt On differetiating w.r.t , we get `(y-k) (dy)/(dx) = 2a " " ` (ii) Again , on differentiating , we get ` (y - k) (d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2)=0" "`…(iii) On putting hte value of `(y-k) ` from Eq. (ii) in Eq. (iii) , we get ` 2a (d^(2)y)/(dx^(2)) + ((dy)/(x))^(3) = 0 ,` which is the required differential equation |
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