Question

If the line (3x+14y+7)+k(5x+7y+6)=0 is parallel to y axis then the value of k is​

Answer 1

$\large\underline{\sf{Solution-}}$

Given equation of line

$\rm :\longmapsto\:3x + 14y + 7 + k(5x + 7y + 6) = 0$

can be rewritten as

$\rm :\longmapsto\:3x + 14y + 7 + k5x + 7ky + 6k = 0$

$\rm :\longmapsto\:(3 + 5k)x +(14 + 7k)y + 7+ 6k = 0$

Since,

This line is parallel to y - axis,

$\rm :\implies\:coefficient \: of \: y \: = 0$

$\rm :\longmapsto\:14 + 7k = 0$

$\rm :\longmapsto\:7k = - 14$

$\bf\implies \:k = - \: 2$

Additional Information :-

1. If line is parallel to x - axis, then slope is zero or coefficient of x is zero.

2. If line is parallel to y - axis, then slope is not defined or coefficient of y is zero.

3. Two lines having slope m and M are parallel iff M = m.

4. Two lines having slope m and M are perpendicular iff Mm = - 1.

5. Three points A, B, C are collinear iff slope of AB = slope of BC = slope of CA.

6. If line makes an angle p with positive direction of x- axis, then m = tanp.