Question

Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes
(1) equal in magnitude and both positive
(2) equal in magnitude but opposite in sign

Answer 1

(1) $\frac{x}{a}+\frac{y}{a}=1$

$\Rightarrow x+y=a$

The above lines passes through a point $(5,6)$ such that,

$5+6=a$

$\Rightarrow a=11$

Therefore, required equation is $x+y=11$

(2) Here there may be two cases

case-1: $\frac{x}{-a}+\frac{y}{a}=1$

$\Rightarrow y-x=a$

The above lines passes through a point $(5,6)$ such that,

$6-5=a$

$\Rightarrow a=1$

Therefore, required equation is $y-x=1$

case-2:$\frac{x}{a}+\frac{y}{-a}=1$

$\Rightarrow x-y=a$

The above lines passes through a point $(5,6)$ such that,

$5-6=a$

$\Rightarrow a=-1$

Therefore, required equation is $x-y=-1$