Question

find the value of k for which the lines are kx-5y+4=0 and 5x-2y+5=0 and are perpendicular to each other

Answer 1

hi friend,

given kx-5y+4=0 and 5x-2y+5=0 and are perpendicular to each other

→slope of first line is -a/b=-k/-5=k/5

→slope of second line is -a/b=5/2

since they are perpendicular ,
the product of slopes should be -1

→k/5×5/2=-1

→k/2=-1

k=-2


I hope this will help u ;)

Answer 2

Step-by-step explanation:

Here, kx – 5y + 4 = 0

⇒ y = kx + 4/5

∴ The slope of the line is k/5.

Also 4x – 2y + 5 = 0

Y = 2x + 5/2

∴ The slope of line is 2.

Since the given lines are perpendicular to each other, we have

(k/5)(2) = - 1 ⇒ k = - 5/2