Question

If 3x + 4y - 5 = 0 and 4x + ky - 8 = 0 are two
perpendicular lines then k is-
(a) 3
(b) 4​

Answer 1

Answer:

3x+4y-5=0_________(I)

4x+ky-8=0_________(II)

$3x+4y-5=0\\ =>4y= -3x+5\\ =>y=\frac{-3x+5}{4}\\ =>y=\frac{-3}{4}x+\frac{5}{4}\_\_\_\_\_\_\_\_(iii)$

Comparing equation (iii) with y=mx+c we get,

m= -3/4

Where m is the slope of the graph representing the equation.

Similarly,

$4x+ky-8=0\\ =>ky= -4x+8\\ =>y=\frac{-4x+8}{k}\\ =>y=\frac{-4}{k}x+\frac{8}{k}\_\_\_\_\_\_\_\_(iv)$

Comparing equation (iv) with y=mx+c we get,

m= -4/k

Where m is the slope of the graph representing the equation.

Let the slope of the first equation be represented by m_(1) and the slope of the second equation be represented by m_(2)

We know that for two perpendicular lines,

$m_{1}×m_{2}= \: -1\\ =>\frac{-3}{4}×\frac{-4}{k}=\: -1\\ =>\frac{3}{k}=\: -1\\ =>3=\: -k\\ =>-k=3\\ =>k=\: -3\_\_\_\_\_\_(ans)$

Answer 2

Answer:

- 3

Explanation:

Given :

Two lines 3 x + 4 y - 5 = 0 and 4 x + k y - 8 = 0

We are asked to find value of k :

We know :

If two lines are perpendicular then their slope product is - 1 :

i.e m₁ m₂ = - 1

Now writing equation in slope intercept form :

i.e. y = m x + c

a). 3 x + 4 y - 5 = 0

= > y = - 3 / 4 x + 5 / 4

We get : m ₁ = - 3 / 4

b). 4 x + k y - 8 = 0

= > y = - 4 / k + 8 / k

Here we get : m₂ = - 4 / k

Now their product :

= > ( - 3 / 4 ) ( - 4 / k ) = - 1

= > 12 = - 4 k

= > k = - 3

Hence we get required answer.