Question

Given the hyperbola (x2/4) – (y2/9) = 1, find the equations for its asymptotes

Answer 1

`(x^2)/(a^2)-(y^2)/(b^2)=1\\\\The\ equations\ of\ asymptotes:\\\\m:y=(b)/(a)x\ and\ n:y=-(b)/(a)x\\-------------------------\\(x^2)/(4)-(y^2)/(9)=1\to(x^2)/(2^2)-(y^2)/(3^2)=1\\\\a=2;\ b=3\to(b)/(a)=(3)/(2)\\\\Answer:\boxed{y=-(3)/(2)x\ and\ y=(3)/(2)x}`