Question

If the lines represented by the equations 3x – y – 5 = 0 and 6x – 2y – p = 0 are parallel, then p is equal to ______.

Answer 1

If the lines represented by the equations 3x – y – 5 = 0 and 6x – 2y – p = 0 are parallel, then p is equal to 10.

Explanation:

For lines ax + by + c = 0 to be parallel, `a_1/a_2 = b_1/b_2 ≠ c_1/c_2`. 

Here `a_1/a_2 = 3/6 = 1/2` and `c_1/c_2 = (-5)/(-p) = 5/p`.

So we need `1/2 ≠ 5/p`, which gives p ≠ 10.