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Answer:
The equation of the straight line passing through the point ( 3,1 )
[tex]\frac{x}{2} + \frac{y}{-2} = 1[/tex]
Step-by-step explanation:
Step(i):-
The equation of the straight line passing through the point ( 3,1 )
[tex]\frac{x}{a} + \frac{y}{b} = 1[/tex]
[tex]\frac{3}{a} + \frac{1}{b} = 1[/tex]
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
[tex]\frac{x}{a} + \frac{y}{b} = 1[/tex]
[tex]\frac{x}{2} + \frac{y}{-2} = 1[/tex]
The equation of the straight line
[tex]\frac{x}{2} + \frac{y}{-2} = 1[/tex]
Verification:-
The equation of the straight line passing through the point (3,1)
[tex]\frac{x}{2} + \frac{y}{-2} = 1[/tex]
Put x =3 and y=1
[tex]\frac{3}{2} + \frac{1}{-2} = 1\\\frac{2}{2} =1\\[/tex]
1 = 1
∴ The point (3,1) is satisfies the equation
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