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FIND THE VALUE OF K SO THAT THE STRAIGHT LINE 2x+ 3y + 4+k(6x - y + 12) = 0 IS PERPENDICULAR TO THE LINE 7x + 5y - 4 = 0.

FIND THE VALUE OF K SO THAT THE STRAIGHT LINE 2x+ 3y + 4+k(6x - y + 12) = 0 IS PERPENDICULAR TO THE LINE 7x + 5y - 4 = 0.

Grade:11

2 Answers

Arun
25763 Points
3 years ago
Dear student
 
if two lines are perpendicular than
m1 * m2 =  -1
 
now
 
for first line-
 
(2+ 6k) x + (3 – k) y + (4 + 12k) = 0
 
m1 =  – (2+6k) / (3 – k)
 
for second line
 
7x +5y – 4 =0
 
m2 = – 7/5
 
now
 
– (2+6k) / (3 – k) * – 7/5 = – 1
 
14 + 42 k = 5 k – 15
37 k =  – 29
 
k = – 29/37
 
Regards
Arun
Deepak Kumar Shringi
askIITians Faculty 4405 Points
3 years ago
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