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For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.

0 5 Views | Posted 4 months ago
Asked by Shiksha User

  • 1 Answer

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    Answered by

    Vishal Baghel | Contributor-Level 10

    4 months ago

    This is a Short Answer Type Questions as classified in NCERT Exemplar

    Sol:

    The  given  equation  are     ax+by+8=0                         …(i)and                                              2x−3y+6=0                         …(ii)From  eqn.(i)  we  get,             ax+by+8=0       ⇒ax+by=−8⇒     a−8x+b−8y=1        ⇒x−8a+y−8b=1So,  the    on  the  axes  are  −8a  and  −8bFrom  eqn.(ii)  we  get,          2x−3y+6=0       ⇒2x−3y=−6⇒          2x−6−3y−6=1        ⇒x−3+y2=1So,  the    on  the  axes  are  −3  and  2.According  to  the  question            −8a=+3     ⇒a=−83and  −8b=−2     ⇒b=+4Hence,  the  required  values  of  a  and  b  are  −83  and  4.

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