wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Show that the equation x26xy+5y2+10x14y+9=0 represent a pair of lines, Find the acute angle between them.

Open in App
Solution

Given equation of straight line is x26xy+5y2+10x14y+9=0.
Compairing with ax2+2hxy+by2+2gx+2fy+c=0, we get
a=1,h=3,b=5,g=5,f=7,c=9
If the equation represents a pair of lines then,
∣ ∣ahghbfgfc∣ ∣=0
D=∣ ∣ahghbfgfc∣ ∣=∣ ∣135 357 579∣ ∣

D=1(4549)(3)(27+35)+(5)(2125)
D=4+2420
D=0
Since, determinant of the given equation is zero, it represents a pair of lines.
Let θ be the acute angle between the pair lines.
tanθ=2h2aba+b

tanθ=∣ ∣2(3)21×51+5∣ ∣

tanθ=2956=246

tanθ=2×26
tanθ=23
θ=tan1(23)=33.69o

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Dot Product
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon