Question

The equation of straight line passing through (-2,-7) and having intercept of length 3 between the straight lines 4x+3y=12 and 4x+3y=3 is

Answer 1

4x + 3y = 12 and 4x + 3y = 3 are parallel lines

Let us first find the distance between the parallel lines

3×4−342+32√=95=1.8

Let A be the angle made by the line with 4x + 3y = 3

tan A=32−1.82√1.8=43

Let m be the slope of the line

tan  A=m−431+4m3=43⇒9m−12=12 + 16m⇒m=−247

Equation of the line:

y−(−7)=−247(x−(−2))

7y + 24x + 97=0