The equation of the straight line passing through the point (4,3) and making intercepts on…

Question

The equation of the straight line passing through the point $(4,3)$ and making intercepts on the co-ordinate axes whose sum is $-1$ is:

Accepted Answer

Let the required line be $${x \over a} + {y \over b} = 1.......\left( 1 \right)$$

then $a+b=-1$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.........\left( 2 \right)$$

$(1)$ passes through $(4,3),$ $$ \Rightarrow {4 \over a} + {3 \over b} = 1$$

$$ \Rightarrow 4b + 3a = ab\,\,...............\left( 3 \right)$$

Eliminating $b$ from $(2)$ and $(3),$  we get

$${a^2} - 4 = 0 \Rightarrow a =  \pm 2 \Rightarrow b =  - 3$$, $1$

$$\therefore$$ Equation of straight lines are

$${x \over 2} + {y \over { - 3}} = 1$$

or $${x \over { - 2}} + {y \over 1} = 1$$

Solutions · 1