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 coincides.

• A. k = $\frac{-2}{15}$
• B. k = $\frac{-15}{2}$
• C. k = $\frac{2}{15}$
• D. k = $\frac{15}{2}$

Answer 1

The correct option is D k = $\frac{15}{2}$

if the path of both the balls coincides.
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ ...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), $\frac{2}{3}=\frac{-5}{-k}=\frac{-4}{-6}$
$\therefore k=\frac{15}{2}$
so, the path of the balls will coincide for k = $\frac{15}{2}$