The equation of the line through the point \((2,3)\) such that its \(x\)-intercept is twice its…
The equation of the line through the point \((2,3)\) such that its \(x\)-intercept is twice its \(y\)-intecept is ......... .
\(x+2 y-8=0\)
\(4 x+y+2=0\)
\(2 x+33 y-46=0\)
\(4 x+3 y-11=0\)
Solution
It is given that line makes \(x\)-intercept twice as compare to \(y\)-intercept, so let the equation of line is
\(\frac{x}{2 a}+\frac{y}{a}=1\) ...(i)
\(\because\) Line (i) passes through \((2,3)\) so
\(\frac{2}{2 a}+\frac{3}{a}=1 \Rightarrow \frac{4}{a}=1 \Rightarrow a=4\)
\(\therefore\) Equation of required line is
\(x+2 y-8=0\)
Hence, option (a) is correct.