Question

If the lines given by $3x+2ky=2$ and $2x+5y+1=0$ are parallel, then the value of $k$ is

• A. $\frac{-5}{4}$
• B. $\frac{2}{5}$
• C. $\frac{15}{4}$
• D. $\frac{3}{2}$

Answer 1

Answer: (C)

$\frac{15}{4}$

Condition for the lines to be parallel is

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Here the equations are

$3x+2ky=2$ and $2x+5y+1=0$

So, $a_1=3,b_1=2k,c_1=-2$ and $a_2=2,b_2=5,c_2=1$

$\therefore \frac{a_1}{a_2}=\frac{3}{2},\frac{b_1}{b_2}=\frac{2k}{5}$ and $\frac{c_1}{c_2}=\frac{-2}{1}=-2$

$\therefore \frac{2k}{5}=\frac{3}{2}$

$\therefore k=\frac{15}{4}$