Question

Find the value of k ifvthe angle between the straight line 4x-y+9=0 andkx-5y-9=0is45°

Answer 1

4x-y+9=0
4x+9=y
so m¹=4
kx-5y-9=0
kx-9=5y
Kx/5 -9=y
so m²= k/5
tan 45=m²-m¹/(1+m¹m²)
1=4-k/5/(1+4(k/5))
1+4(k/5)=4-k/5
4k/5+k/5=4-1
5k/5=3
k=3

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