Let `l` be the line belonging to the family of straight lines `(a + 2b)x+ (a - 3b)y +a-8b = 0, a, b in R`, which is farthest from the point `(2, 2),` then area enclosed by the line `L` and the coordinate axes is

Options

A. 4/3 sq. units
B. 9/2 sq. units
C. 49/8 sq. units
D. none of these

Answer

C

Explanation

Also, this line x+4y+7 =0 meets the axes C(-7,0) and D(0, -7/4). Then the area of triangle OCD is (1/2)|(-7)(-7/4)| or 49/8.