Q no. 6

​Q6. If f(x, y) = x2 + y2 – 3x + 5y + 3, then minimum value of f (x, y ) is -

    ​ ( A ) 13 2                                             ( B ) - 11 2                                     ( C )   7 2                                       ( D )   9 2
      Equation of the angle bisector of the  angle between the lines 11x + 12 y – 6 = 0 and in which point (–2, 3 )       line, is given by -

    (A) 23 x + 23 – 1 = 0                              (B) x – y + 11 =0

    (C) x + y + 11 = 0                                   (D) 23x – 23y – 1 = 0
 

Hi, fx,y= x2+y2-3x+5y+3 = x2-3x+y2+5y+3= x2-3x+94-94+y2+5y+254-254+3=x2-3x+94+y2+5y+254+3-94-254=x-322+y+522+3-172=x-322+y+522-112Now x-322,y+522 being a square quantity they will always be greater than or equal to zero so x-322+y+522-1120+0-112-112

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