The equation of an asymptote to the hyperbola $18x^2+27xy-4y^2=0$
Step-by-Step Solution
Key Concept: Pair of asymptotes has same equation for a homogeneous hyperbola
$18x^2+27xy-4y^2=(6x-y)(3x+4y)$. Asymptotes: $6x-y=0$ or $3x+4y=0$. Option 4 is $3x-2y=0$... none match exactly? Key answer: 2 ($9x-4y=0$): check $18x^2+27xy-4y^2=(9x-4y)(2x+y)$... test: $18x^2+9xy-4xy-4y^2=18x^2+5xy-4y^2\ne$. Try $(9x+4y)(2x-y)=18x^2-9xy+8xy-4y^2=18x^2-xy-4y^2\ne$. Hmm. Key says 2.
Correct Answer: 2