if the line (3x+14y+7)+k(5x+7y+6)=0 is parallel to Y Axis then the value of K is
Answers
Step-by-step explanation:
Given equation of line
\rm :\longmapsto\:3x + 14y + 7 + k(5x + 7y + 6) = 0:⟼3x+14y+7+k(5x+7y+6)=0
can be rewritten as
\rm :\longmapsto\:3x + 14y + 7 + k5x + 7ky + 6k = 0:⟼3x+14y+7+k5x+7ky+6k=0
\rm :\longmapsto\:(3 + 5k)x +(14 + 7k)y + 7+ 6k = 0:⟼(3+5k)x+(14+7k)y+7+6k=0
Since,
This line is parallel to y - axis,
\rm :\implies\:coefficient \: of \: y \: = 0:⟹coefficientofy=0
\rm :\longmapsto\:14 + 7k = 0:⟼14+7k=0
\rm :\longmapsto\:7k = - 14:⟼7k=−14
\bf\implies \:k = - \: 2⟹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.
Step-by-step explanation:
(3× + 5×) (14y+7y) (7+6)
(8) (21) (13)
(8+21=29)(29+13=42)
(29÷42)
ans 0.6904761905