InterviewSolution
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InterviewSolution
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Line joining `A(bcosalpha,bsinalpha)` and `B(acosbeta,asinbeta)`, is produced to the point `M(x,y)` such that `AM:MB=b:a` then `xcos((alpha+beta)/2)+ysin((alpha+beta)/2) =`A. (-1)B. 0C. 1D. `a^(2)+b^(2)` |
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Answer» Correct Answer - B Clearly , M divides AB expternally in the ratio `b:a`. `:. x=(b(acos beta)-a(b cos alpha))/(b-a) and,y=(b(a sin beta)-a(b sin alpha))/(b-a)` `rArr(x)/(y)=(cos beta-cos alpha)/(sin beta- sin alpha)` `rArr (x)/(y)(2 "sin" (alpha+beta)/(2) "sin"(alpha-beta)/(2))/(-2 "sin" (alpha+beta)/(2) "sin"(alpha-beta)/(2))` `rArr x "cos" ((alpha+beta)/(2)) + y "sin"((alpha+beta)/(2))=0` |
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