How many straight lines passing through (2,3) form a triangle with coordinate axes, whose area is 12 sq. units?

1 Answer
P dilip_k
Aug 31, 2017

One

Explanation:

  • Let the equation of the straight line passing through #(2,3)# be #y-3=m(x-3)#,where #m# represents the slope of the straight line.

  • Transforming the above equation in intercept form we have #x/((2m-3)/m)+y/(3-2m)=1#

  • So x-intercept #=(2m-3)/m# and y-intercept # =(3-2m)#

  • Area of the triangle formed by the straight line and intercepts from axes is given by
    #1/2xx(2m-3)/mxx(3-2m)=12#

#=>4m^2+12m+9=0#

#=>(2m+3)^2=0#

#=>m=-3/2#

As m has got only one real value, we can say that only one straight line passing through #(2,3)# is possible under the given condition.

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