Question

The line equally inclined to the coordinate axes and equidistant from points A(1,-2) and B (3,4) is

• A. $x+y=2,x+y=3$
• B. $x-y=3,x-y=1$
• C. $x-y=1,x+y=3$
• D. $x+y=2,x-y=3$

Answer 1

The correct option is C $x-y=1,x+y=3$

given,

the two points $\left(A\right)(1,-2)$ and $\left(b\right)(3,4)$

and the line

$\frac{x}{a}+\frac{y}{b}=1$ [are equally inclined to cordinate axis]

$a=b=k$

$x+y=k$

Now equating the equistance from $A$ and $B$ |$1\frac{-2-k}{\sqrt{2}}|$=|$3\frac{+4-k}{\sqrt{2}}|$

$r=1-k=\pm (7-k)$

$-1-k=7-k\text{or}-1-k=-7+k$

$-1+7=2k$

$k=3$

$x+y=3$ and $x-y=1=$ option $C$