Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $O A B$ is 12 sq. units. If the line passes through the point $(2,3)$, then the equation of the line is

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Aicharya · Accepted Answer

Area of $	riangle A O B=12$ sq. units $\begin{array}{ll} & \frac{1}{2} a b=12 \ 	herefore \quad & a b=24 \ 	herefore \quad & b=\frac{24}{a}...(i) \end{array}$ Equation of line in point slope form is $\begin{aligned} & y-a=\frac{-a}{b}(x-0) \ & y-a=\frac{-a x}{\frac{24}{a}} \end{aligned}$ ...[from (i)] $y-\mathrm{a}=\frac{-\mathrm{a}^2 x}{24}...(ii)$ Since line passes through $(2,3)$ $\begin{aligned} & 	herefore \quad 3-a=\frac{-a^2(2)}{24} \ & \quad \Rightarrow 3-a=\frac{-a^2}{12} \ & \ & \quad \Rightarrow a^2-12 a+36=0 \ & \ & \quad \Rightarrow(a-6)^2=0 \ & \quad \Rightarrow a=6 \ & 	herefore \quad \ & 	herefore=\frac{24}{6}=4...[from(i)] \end{aligned}$ Required equation of line is $\begin{aligned} & y-6=\frac{-36 x}{24}...[from(ii)] \ & 2 y-12=-3 x \ & \Rightarrow 3 x+2 y-12=0 \ & \Rightarrow 3 x+2 y=12 \end{aligned}$ ...[from (ii)]

Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $O A B$…

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