Find the equation of the straight line passing through the point (4,3) and making intercepts on the coordinate axes whose sum is -1.

Options

A. `(x)/(2) - (y)/(3) = 1 ` and `(x)/(-2) + (y)/(1) = 1`
B. `(x)/(2) - (y)/(3) = -1` and `(x)/(-2) + (y)/(1) = -1`
C. `(x)/(2) + (y)/(3) = 1` and `(x)/(2) + (y)/(1) = 1`
D. `(x)/(2) + (y)/(3) = -1` and `(x)/(-2) + (y)/(1) = -1`

Answer

A

Explanation

Let the equation of the line be
`(x)/(a) + (y)/(b)=1 " " … (i)`
It passses through (4,3)
`therefore (4)/(a) + (3)/(b) = 1 " " … (ii)`
It is given that a + b = - 1 `" " … (iii)`
Solving these equations , we get
(a =- 2 , b = 1) or , (a = 2 , b = -3)
Substituting the value of a and b in (i) , we get
`(x)/(-2) + (y)/(1) = 1` and `(x)/(2) + (y)/(-3) = 1`
ALTER Clearly , lines in option (a) pass through (4,3) and the sum of their intercepts on the coordinates axes is -1 . Hence , option (a) is correct .