Question

Let d be the distance between the parallel lines 3x - 2y + 5 = 0 and 3x - 2y + 5 + 2√13 = 0. Let L1 = 3x - 2y + k1 = 0 (k1 > 0) and L2 = 3x - 2y + k2 = 0 (k2 > 0) be two lines that are at the distance of $\frac{4d}{√13}$ and $\frac{3d}{√13}$ from the line 3x - 2y + 5y = 0. Then the combined equation of the lines L1 = 0 and L2 = 0 is:

• A. (3x - 2y)2 + 24(3x - 2y) + 143 = 0
• B. (3x - 2y)2 + 8(3x - 2y)+ 33 = 0
• C. (3x - 2y)2 +12(3x-2y) + 13 = 0
• D. (3x - 2y)2 +12(3x-2y) + 1 = 0

Answer 1

Answer: (A)

(3x - 2y)2 + 24(3x - 2y) + 143 = 0

Answer 2

The correct option is (A) (3x - 2y)2 + 24(3x - 2y) + 143 = 0