Question

Find the angle between the following pairs of lines x^2+6xy +9y^2-4x +12y-5 =0​

Answer 1

Answer:

x

2

+6xy+9y

2

+4x+12y−5=0

Step-by-step explanation:

x

2

+6xy+9y

2

+4x+12y−5=0

Comparing the equation with the general equation of second degree gives

a=1,b=9,h=3,g=2,f=6,c=−5

Angle between a pair of straight lines that is tanθ=

∣

∣

∣

∣

∣

∣

​

 

a+b

2

h

2

−ab

​

​

 

∣

∣

∣

∣

∣

∣

​

tanθ=

∣

∣

∣

∣

∣

​

 

1+9

2

9−1×9

​

​

 

∣

∣

∣

∣

∣

​

=

9

0

​

tanθ=0

⇒θ=tan

−

(0)=0

∘

Angle between the pair of straight lines is zero therefore the lines are parallel.

Hence proved