Correct option (a)
Explanation :
The given hyperbola is
x2/1/4 - y2/1/9 = 1
and the line is
y = (5/4)x + 7/4
Any line parallel to this line is
y = (5/4)x + c
This will touch the hyperbola which implies that
Hence, the tangents are
Hence, the distance between these tangents is