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 both the balls collide.

• A. The balls will collide for all the real value of k except $\frac{15}{2}$
• B. The balls will collide for all the real value of k except $\frac{2}{15}$
• C. The balls will collide for all the values of k
• D. The ball will collide at k = $\frac{15}{2}$

Answer 1

The correct option is A The balls will collide for all the real value of k except $\frac{15}{2}$

For the balls to collide, the path of both the balls should intersect.
$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$ ...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), $\frac{2}{3}\ne \frac{-5}{-k}$
$\therefore k\ne \frac{15}{2}$
so, the balls will collide for all the real value of k except $\frac{15}{2}$