Q.

Find the value of k, if the angle between the straight lines 4x–y+7=0 and kx–5y–9=0 is 45°.

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Detailed Solution

If   θ is angle between the st.lines
a1x+b1y+c1=0 and a2x+b2y+c2=0  then
cosθ=a1a2+b1b2a12+b12a22+b22
Given st.lines 4x – y + 7 = 0; Kx – 5y – 9 = 0
Where θ=45 ,a1=4,b1=-1,a2=k,b2=-5Now cos45=4k+516+1k2+25 S.O.B.S. 15K2+80K375=03K2+16K75=0(K3)(3K+25)=0K=3 (or )k=25/3K=3 (or) k=253

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