Straight Line Question 65

Question: The equation of straight line passing through $ (-a,\ 0) $ and making the triangle with axes of area ?T? is [RPET 1987]

Options:

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

Show Answer

Answer:

Correct Answer: B

Solution:

  • If the line cuts off the axes at A and B, then area of triangle is $ \frac{1}{2}\times OA\times OB=T $
    Þ $ \frac{1}{2}.a.OB=T\Rightarrow OB=\frac{2T}{a} $ Hence the equation of line is $ \frac{x}{-a}+\frac{y}{2T/a}=1 $

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