Question

Find k, if the line 4x - y = 1 is perpendicular to the line 5x - ky = 2?

Options:

1) 20

2) -20

3) 4

4) -4

Answer 1

Hi ,

4x - y = 1 -----( 1 )

Slope of above line = m1

m1 = - ( x - coefficient ) /( y-coefficient)

m1 = - 4/( - 1 ) = 4

5x - ky = 2 ------( 2 )

Slope of the line = m2 = - 5/( - k )

m2 = 5/k

According to the problem given ,

Two lines are perpendicular each

other ,

Therefore ,

m1 × m2 = -1

4 × ( 5/k ) = -1

20/k = -1

k = -20

I hope this helps you.


:)

Answer 2

slope of line 4x-y=1
=>y=4x-1
slope=(4/1)
slope of line 5x-ky=2
=>y=(2-5x)/k
=>y=(-5/k)x+2/k
slope is -(5/k)
But, we know that the product of median of 2 perpendicular line=-1
so,
-5/k×4/1=-1
-20/k=-1
k=20