Question

15. Find the equation of the straight line passing through the point (5, -3) and whose
intercepts on the axes are equal in magnitude but opposite in sign.

Answer 1

Solution:-

given by:- the equation of the straight line passing through the point (5, -3) and whose
intercepts on the axes are equal in magnitude but opposite in sign.

we have :-
$intercpt \: \\ \frac{x}{a} + \frac{y}{b} = 1 \\ intercepts \: are \: equal \: in magnitude \: but \: opposite \: in \: sign. \\ \\ x- \: intercept \: (a) \: = t \\ \\ y-intercept \: (b) \: = \: -t \\ \\ The \: required \: line \: is \: passing \: through \: the \: point \: (5,-3) \\ \\ \frac{5}{t} + \: \frac{ - 3}{ - t} = \: 1 \\ \\ \frac{5}{t} + \frac{3}{t} = \: 1 \\ \\ \frac{(5 + 3)}{t} = \: 1 \\ \\ \frac{8}{t} = \: 1 \\ 8 \: = \: t \\ t \: = \: 8 \\ \frac{x}{8} + \: \frac{y}{ - 8} = \: 1 \\ \\ \frac{(x - y)}{8} = 1 \\ \\ x \: - \: y \: = \: 8 \\ \\ (x \: - \: y \: - \: 8 \: = \: 0)ans$
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Answer 2

Solution :

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Equation of a line whose ,

x-intercept = a , and

y-intercept = b , is

x/a + y/b = 1
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Here ,

x-intercept ( a ) = n ,

y-intercept (b ) = -n ,

x/n + y/(-n) = 1 which is passing

through the point ( 5 , -3 ) [ given ]

5/n + (-3)/(-n) = 1

=> 5/n + 3/n = 1

=> 8/n = 1

=> n = 8

Therefore ,

x-intercept (a) = n = 8

y-intercept ( b ) = -n = -8

Required equation ,

x/8 - y/8 = 1

=> x - y = 8

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