MATHEMATICS - OBJECTIVE -2

6. Area of triangle formed by the lines x + y = 3 and angle bisectors of the pair of straight lines  x² - y²+2y=1 is

(a) 2 sq units           (b) 4 sq units

(c) 6 sq units            (d) 8 sq units

answer (a)

Answer explanation: x+y =3 so for plotting x-y graph,at x=0,y=3  &  at y=0,x=3 (using this co-ordinates graph has been plotted)

Now to plot line for next equation ,x² - y²+2y=1

at x=0,y=1(first solution) and x=3,y=4 (second solution). let us plot graph using first solution,x=0,y=1 Only this solution bisects the first equation line x+y=3 ;so this is only the valid solution  as per the question above.

area of triangle formed by bisection as shown in figure =1/2 x base x height 

=1/2 x 2 x (3-1)

= 1/2 x 2 x2

 =2 sq units

This type of graph is used in probability analysis ,where one solution gives the right idea about the situation .Hence the graph shown above often indicates the algebrical solution rather than the angular aspect .Probability analysis is maximum at the above plotted solution ,while the second solution indicates lack of confidence as per probability distribution of the selected sample lot .Hence this graph is a probability analysis study of the above said algebric equation along with the given parameters.