Question

if the acute angle between the lines
kr + y + 9 = 0 and y - 3x = 4 is 45", then find the value of k​

Answer 1

kx+y+9=0

y=−kx−9

Thus, slope of the line m1=−k

Similarly, y=3x+4

Slope of the line is m2=3

Therefore, angle between the lines is

tanθ=∣∣∣∣∣1+m1m2m2−m1∣∣∣∣∣

=∣∣∣∣∣1−3k3+k∣∣∣∣∣

=∣∣∣∣∣1−3kk+3∣∣∣∣∣

But θ=45o

 

∴tanθ=1

⇒1−3kk+3=±1

⇒k+3=±(1−3k)

Case I

k+3=1−3k

i.e. 

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