Question
The equation of straight line passing through $$\left( { - a,\,0} \right)$$ and making a triangle with the axes of area $$T$$ is :
A.
$$2Tx + {a^2}y + 2aT = 0$$
B.
$$2Tx - {a^2}y + 2aT = 0$$
C.
$$2Tx - {a^2}y - 2aT = 0$$
D.
None of these
Answer :
$$2Tx - {a^2}y + 2aT = 0$$
Solution :
If the line cuts off the axes at $$A$$ and $$B,$$ then the area of triangle is
$$\eqalign{
& \frac{1}{2} \times OA \times OB = T \cr
& {\text{or }}\frac{1}{2} \times a \times OB = T \cr
& {\text{or }}OB = \frac{{2T}}{a} \cr} $$
Hence, the equation of line is $$\frac{x}{{ - a}} + \frac{y}{{\frac{{2T}}{a}}} = 1\,\,{\text{or }}2Tx - {a^2}y + 2aT = 0$$