Question

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

Answer 1

$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\\\\The\ equations\ of\ asymptotes:\\\\m:y=\dfrac{b}{a}x\ and\ n:y=-\dfrac{b}{a}x\\-------------------------\\\dfrac{x^2}{4}-\dfrac{y^2}{9}=1\to\dfrac{x^2}{2^2}-\dfrac{y^2}{3^2}=1\\\\a=2;\ b=3\to\dfrac{b}{a}=\dfrac{3}{2}\\\\Answer:\boxed{y=-\frac{3}{2}x\ and\ y=\frac{3}{2}x}$