Question

find the equation of line which passes through point (5,6) and has intercepts on the axes equal in magnitude but opposite in sign.​

Answer 1

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Given :-

A line passes through the point (5, 6) and makes intercepts on the axes equal in magnitude but opposite in sign.

Let intercept on x - axis be 'a'.

=> intercept on y - axis be '- a'.

To find:-

Eqution of line

$\large\bold\red{Formula \: used :-}$

$intercept \: form \: of \: a \: line \: \\ \frac{x}{a} + \frac{y}{b} = 1$

where a = intercept on x axis

and b = intercept on y axis.

$\large\bold\red{Solution:- }$

$\small\bold\red{So \: equation \: of \: line \: using \: intercept \: form \: is }$

$\small\bold\red{ \frac{x}{a} + \frac{y}{ - a} = 1} \\ \small\bold\red{ = > \frac{x}{a} - \frac{y}{a} = 1 } \\ \small\bold\red{ = > \: x - y = a}.........(1) \\ \small\bold\blue{now \: (1) \: passes \: through \: (5, 6)} \\ \small\bold\red{5 - 6 = a \: = > \: a = - 1} \\ so \: equation \: (1) \: become \\ x - y = - 1 \\ = > \: x - y + 1 = 0$

$\huge \fcolorbox{black}{yellow}{♛hope \: it \: helps \: you♛}$