Angle between the pair of straight lines is zero therefore the lines are parallel.
What is parallel lines?
Parallel lines can be defined as two lines in the same plane that their angle of inclidation is equal and never meet.
Given,
x²+6xy+9y²-4x+12y-5=0
Comparing the equation with the general equation of 2nd degree
ax² + ay² + 2gx + 2fy + c = 0
so a=1, b=9, h= 3, g=-2, f=6, c=5
Angle between a pair of straight lines that is
tan∅=[tex]\frac{2\sqrt{h^{2} -ab} }{a+b}[/tex]
tan∅=[tex]\frac{2\sqrt{3^{2} -(1)(9)} }{1+9}[/tex]
tan∅=0°
∅=0°
Hence Angle between the pair of straight lines is zero therefore the lines are parallel.
Learn more about straight lines
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