Question

1. Problem: Find the equation of the straight line passing through the point (2,3) and making
non-zero intercepts on the axes of coordinates whose sum is zero.​

Answer 1

SOLUTION :-

TO DETERMINE :-

The equation of the straight line passing through the point (2,3) and making non-zero intercepts on the axes of coordinates whose sum is zero.

EVALUATION :-

Let the equation of the line which makes non-zero intercepts on the coordinate axes is

$\displaystyle \sf{ \frac{x}{a} + \frac{y}{b} = 1 } \: \: \: ....(1)$

Since the sum of intercepts is zero

Therefore

$\sf{a + b = 0 } \: \: \:$

$\implies \sf{b = - a} \: \: \: ......(2)$

Again the line (1) passes through the point (2,3)

Therefore

$\displaystyle \sf{ \frac{2}{a} + \frac{3}{b} = 1 } \: \:$

Using Equation (2) we get

$\displaystyle \sf{ \frac{2}{a} + \frac{3}{ - a} = 1 } \: \:$

$\implies \displaystyle \sf{ \frac{2}{a} - \frac{3}{a} = 1 } \: \:$

$\implies \displaystyle \sf{ - \frac{1}{a} = 1 } \: \:$

$\implies \displaystyle \sf{a = - 1 } \: \:$

From Equation (2) we get

$\sf{b = 1}$

From Equation (1) we get the equation of the required line as :

$\displaystyle \sf{ \frac{x}{ - 1} + \frac{y}{1} = 1 } \: \: \:$

$\implies \sf{x - y = - 1}$

FINAL ANSWER :-

The required equation of the line is

$\boxed{ \: \: \sf{x - y = - 1} \: \: }$

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Answer 2

Answer:

Step-by-step explanation:

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