The equation of straight line passing through (-2,-7) and having an intercept of length 3 between the straight lines : 4x + 3y = 12 , 4x + 3y = 3 are : (A) 7x + 24y + 182 = 0 (B) 7x + 24y + 18 = 0 (C) x + 2 = 0 (D) x - 2 = 0

Explanation

Given lines are
`4x+3y-12=0 " "(1)`
`"and "4x+3y-3=0 " "(2)`
Given AB=3.
The distance between parallel lines (1) and (2),
`AL= (|-12+3|)/(sqrt(4^(2) + 3^(2))) = (9)/(5)`
` "From" Delta "ALB, we get"`
`LB^(2) =AB^(2)-AL^(2)`
`= 3^(2) - (81)/(25) = 9 xx (16)/(25)`
`therefore LB = (12)/(5)`
`tan alpha = (AL)/(LB) = (3)/(4)`
`"Also, tan" theta = "Slope of line" (1) = -(4)/(3)`
Let the slope of PB be m. Now,
`tan alpha = (3)/(4) = |(m-(-4//3))/(1+m(-4//3))| = |(3m+4)/(3-4m)|`
` "or " m = oo or m = -(7)/(24)`
Therefore, the equation of the line is
`x+2=0 " and "y+7 = -(7)/(24)(x+2)`
` "or " x+2=0 " and " 7x +24y+182 =0`