Question

The given figure shows the path of two balls.

If path followed by the blue ball and the red ball is 2x-5y=4, and 3x-ky=6 respectively.


Determine the value of 'k' for which the path of the balls is parallel.

• A. $k=\frac{2}{15}$
• B. $k=\frac{15}{2}$
• C. It is not possible for the balls to have parallel path
• D. $k=\frac{-15}{2}$

Answer 1

The correct option is C It is not possible for the balls to have parallel path

If the path of both the balls is parallel,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$ ...Eq (i)
Given 2x-5y=4, and 3x-ky=6
Here, $a_1=2,b_1=-5,c_1=-4$
and $a_2=3,b_2=-k,c_2=-6$

From Eq (i), $\frac{2}{3}=\frac{-5}{-k}\ne \frac{-4}{-6}$
but we can see that $\frac{2}{3}=\frac{-4}{-6}$ (i.e. $\frac{a_1}{a_2}=\frac{c_1}{c_2}$)
so, it is not possible for the balls to have parallel path.