Question

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

• A. $20$
• B. $-7$
• C. $7$
• D. $-20$

Answer 1

The correct option is B

$-7$

Explanation for the correct option:

In the question, it is given that the line $2x-3y+k=0,3x-4y-13=0$ and $8x-11y-33=0$ are concurrent.

So, the condition for lines to be concurrent is $\left[\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right]=0$.

So,

$\left[\begin{array}{ccc}2& -3& k\\ 3& -4& -13\\ 8& -11& -33\end{array}\right]=0$

Expand the determinant with respect to $R_1$.

$$\begin{gathered} 2(132-143)+3(-99+104)+k(-33+32)=0 \\ \Rightarrow -22+15-k=0 \\ \Rightarrow k=-7 \end{gathered}$$

Therefore, the required value of $k$ is $-7$.

Hence, option B is the correct answer.