2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Straight Line

JEE Main & Advanced Mathematics Straight Line Question Bank Problems related to triangle and quadrilateral Locus

  • question_answer
    Area of the parallelogram whose sides are \[x\cos \alpha +y\sin \alpha =p\] \[x\cos \alpha +y\sin \alpha =q,\,\,\] \[x\cos \beta +y\sin \beta =r\]  and \[x\cos \beta +y\sin \beta =s\] is

    A)            \[\pm (p-q)(r-s)\,\text{cosec}(\alpha -\beta )\]                         

    B)            \[(p+q)(r-s)\,\text{cosec }(\alpha +\beta )\]

    C)            \[(p+q)(r+s)\,\text{cosec }(\alpha -\beta )\]                              

    D)            None of these

    Correct Answer: A

    Solution :

               Use,    Area = \[{{p}_{1}}.{{p}_{2}}\text{cosec}\theta \]                    where \[\tan \theta =\frac{-\tan \alpha +\tan \beta }{1+\tan \alpha \tan \beta }=\tan (\beta -\alpha )\]                    \ \[\theta =\beta -\alpha ,{{p}_{1}}=p-q,{{p}_{2}}=r-s\].


You need to login to perform this action.
You will be redirected in 3 sec spinner