Question

The value of k so that the lines 2x – 3y + k = 0, 3x – 4y – 13 = 0 and 8x – 11y – 33 = 0 are concurrent, is

• A. 7
• B. -7
• C. 5
• D. -5

Answer 1

The correct option is B

-7

Since the given lines are concurrent, therefore,

$\left|\begin{array}{ccc}2& -3& k\\ 3& -4& -13\\ 8& -11& -33\end{array}\right|$

$\Rightarrow$ 2(132 – 143) + 3(–99 + 104) + k(–33 + 32) = 0

$\Rightarrow$ –22 + 15 – k = 0 or k = –7