Question

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

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

Answer 1

The correct option is A $\frac{15}{4}$

Condition for parallel lines is
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Given 3x + 2ky – 2 = 0
And 2x + 5y – 1 = 0
Here, $a_1=3,b_1=2k,c_1=-2$
and $a_2=2,b_2=5,c_2=-1$

From Eq (i), $\frac{3}{2}=\frac{2k}{5}$
$\therefore k=\frac{15}{4}$

Also, $\frac{c_1}{c_2}=\frac{-2}{-1}=2$

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