Question

the angle between the lines 4x-y+7=0,kx-5y-9=0 is 45degrees k=​

Answer 1

Answer:The acute angle between the given lines is 45°.

Answer 2

The value of k is 3.

Given,

The angle between two lines 4x-y+7=0 and kx-5y-9=0 is 45°.

To Find,

The value of k.

Solution,

The formula for calculating the angle between two lines is

tan θ = |(m₁-m₂)/(1+m₁*m₂)|

where m₁ and m₂ are the slopes of the line.

tan 45 = 1

For, 4x-y+7=0 m₁ = 4

For, kx-5y-9 = 0 m₂ = k/5

So,

(4-k/5) = (1+4k/5)

20-k = 5+4k

15 = 5k

k = 15/5 = 3

Hence, the value of k is 3.

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