Final answer:
The distance between L1 and L2 is |(b-3)/c + 1/5| / sqrt(1 + (-1/5)^2) and the correct answer is D. 23/√15.
Step-by-step explanation:
Given line L1: x/5 + y/b = 1 passes through point M(13,32). Line L2 is parallel to L1 and has equation
x/c + y/3 = 1.
Two lines are parallel if their slopes are equal. To find the slope of L1 and L2, we need to rewrite the equations in the form y = mx + b, where m is the slope.
For L1, rearranging the equation gives us
y = -x/5 + 1.
The slope of L1 is -1/5. T
herefore, L2 must also have a slope of -1/5.
The equation of L2 gives us y = -x/c + 3.
Since the slopes are equal, the distance between L1 and L2 is the perpendicular distance between them.
Thus, the distance between L1 and L2 is given by the formula |(b-3)/c + 1/5| / sqrt(1 + (-1/5)^2).
Therefore, the correct answer is D. 23/√15.