Equation of straight line passing through ( - a,0) and making triangle with axes of area ‘ T &

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9.Straight Line

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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

Solution

(b) If the line cuts off the axes at $A$ and $B$, then area of triangle is $\frac{1}{2} \times OA \times OB = T$

==> $\frac{1}{2}.a.OB = T \Rightarrow OB = \frac{{2T}}{a}$

Hence the equation of line is $\frac{x}{{ – a}} + \frac{y}{{2T/a}} = 1$

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

Standard 11

Mathematics

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