Question

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

Answer 1

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.