Question

The equation of straight line passing through $(-a,0)$ and making the triangle with 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 1

Answer: (B)

$2Tx-a^{2}y+2aT=0$

Area of triangle $=\frac{1}{2}\times base\times height$

$⟹Area=\frac{1}{2}\times a\times h=T⟹h=\frac{2T}{a}$

Equation of line : $y-\frac{2T}{a}=\frac{\frac{2T}{a}-0}{0-(-a)}\times (x-0)$ $⟹a^{2}y-2aT=2Tx⟹2Tx-a^{2}y+2aT=0$

(Since equation of line joining two points $(x_0,y_0)$ and $(x_1,y_1)$ is $y-y_0=\frac{y_1-y_0}{x_1-x_0}\times (x-x_0)$)