# Chapter 4 - 4.3 - Conics - 4.3 Exercises - Page 339: 65

$x^2-\frac{y^2}{9}=1$

#### Work Step by Step

Transverse axis is horizontal. $(±a,0)=(±1,0)$ $a=1$ The equation of the asymptotes when transverse axis is horizontal: $y=±\frac{b}{a}x$ The equation of the asymptotes: $y=±3x$ So: $\frac{b}{a}=3$ $\frac{b}{1}=3$ $b=3$ Standard form when transverse axis is horizontal: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ $\frac{x^2}{1^2}-\frac{y^2}{3^2}=1$ $\frac{x^2}{1}-\frac{y^2}{9}=1$ $x^2-\frac{y^2}{9}=1$

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