Question

13. Find the equation of the straight line passing through the point (3, 4) and has
intercepts which are in the ratio 3 : 2

Answer 1

Solution:-

given by:- the straight line passing through the point (3, 4) and has intercepts which are in the ratio 3 : 2

we have ,

$intercepts \: for m \: \: \\ \frac{x}{a} + \frac{y}{b} = 1 \\ \\ here \: intercepts \: are \: in \: the \: ratio \: 3 : 2 \\ \\ So \: \: x-intercept \: (a) \: = \: 3 t \\ \\ y-intercept \: (b) = \: 2 t \\ \\ \frac{3}{3t} + \frac{4}{2t} = 1 \\ \\ \frac{3 + 6}{3t} = 1 \\ \\ = 3 \\ \\ So \: ,x-intercept \: (a) = \: 3 t = \: 3 \times 3 = 9 \\ \\ y-intercept \: (b) = \: 2 t = \: 2 \times 3 = \: 6 \\ \\ \frac{x}{9} + \frac{y}{6} = 1 \\ \\ \frac{2x + 3y}{18} = 1 \\ \\ 2 x \: + \: 3 y = \: 18 \\ \\ 2 x \: + \: 3 y \: - \: 18 = \: 0$
equation of the straight line (2x+3y-18 =0) ans

Answer 2

Solution :

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Equation of a line whose

x - intercept = a , y-intercept = b ,

is

x/a + y/b = 1

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Given ratio of intercepts a : b = 3:2

Let x- intercept = a = 3m

y-intercept ( b ) = 2m ,

x/3m + y/2m = 1 which is passing

through ( 3 , 4 ) , we get

3/3m + 4/2m = 1

=> 1/m + 2/m = 1

=> 3/m = 1

=> m = 3

Therefore ,

x-intercept = a = 3m = 3 × 3 = 9

y-intercept = b = 2m = 2 × 3 = 6

Equation is

x/9 + y/6 = 1

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