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

1 Answer
Aug 31, 2017

One

Explanation:

  • Let the equation of the straight line passing through (2,3) be y3=m(x3),where m represents the slope of the straight line.

  • Transforming the above equation in intercept form we have x2m3m+y32m=1

  • So x-intercept =2m3m and y-intercept =(32m)

  • Area of the triangle formed by the straight line and intercepts from axes is given by
    12×2m3m×(32m)=12

4m2+12m+9=0

(2m+3)2=0

m=32

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.