Q118 / 170 · Manipal (MET) 2015 · Mathematics
The equations of the straight lines passing through the point $(4,3)$ and making intercepts on the coordinate axes whose sum is -1 , is
- Correct answerA$\frac{x}{2}-\frac{y}{3}=1$ and $\frac{x}{-2}+\frac{y}{1}=1$
- B$\frac{x}{2}-\frac{y}{3}=-1$ and $\frac{x}{-2}+\frac{y}{1}=-1$
- C$\frac{x}{2}+\frac{y}{3}=1$ and $\frac{x}{2}+\frac{y}{1}=1$
- DNone of the above
Solution
Let the equation of the line be
$\frac{x}{a}+\frac{y}{b}=1$ ...(i)
which passes through $(4,3)$.
$\therefore \quad \frac{4}{a}+\frac{3}{b}=1$ ...(ii)
It is given that $a+b=-1$ ...(iii)
On solving Eqs. (i) and (ii), we get
$a=-2, b=1 \text { or } a=2, b=-3$
On substituting the values of $a$ and $b$ in Eq. (i), we get
$\frac{x}{-2}+\frac{y}{1}=1 \text { and } \frac{x}{2}+\frac{y}{-3}=1$
Hence, the correct answer is option: 'A'.