Question

34. Find the equation of the straight line which

.
passes through the point (3,1) and makes
intercepts on the axes the difference of
whose length is 4.

Answer 1

The equation of the straight line passing through the point ( 3,1 )

`(x)/(2) + (y)/(-2) = 1`

Explanation:

Step(i):-

The equation of the straight line passing through the point ( 3,1 )

`(x)/(a) + (y)/(b) = 1`

`(3)/(a) + (1)/(b) = 1`

3b + a = ab ...(i)

Given the difference of length is 4

a-b = 4

b = a - 4 ...(ii)

Step(ii):-

substitute b=a-4 in equation (i) , we get

3( a-4 ) + a = a (a-4)

3a - 12+ a = - 4 a + a²

a² - 8 a + 12 =0

Find the factors of 'a'

a² - 6a -2a +12 =0

a (a-6) -2(a-6) =0

a =2 and a=6

we know that a-b =4

put a = 2

2 - b =4

b = -2

The equation of the straight line whose intercepts on the axes

`(x)/(a) + (y)/(b) = 1`

`(x)/(2) + (y)/(-2) = 1`

The equation of the straight line

`(x)/(2) + (y)/(-2) = 1`

Verification:-

The equation of the straight line passing through the point (3,1)

`(x)/(2) + (y)/(-2) = 1`

Put x =3 and y=1

`(3)/(2) + (1)/(-2) = 1\\(2)/(2) =1\\`

1 = 1

∴ The point (3,1) is satisfies the equation