Find the equation of the hyperbola satisfying | vedclass

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(A) The vertices are $(\pm 2, 0)$,which lie on the $x$-axis. Thus,the equation of the hyperbola is of the form $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{

Vedclass · Accepted Answer

$\frac{x^{2}}{4} - \frac{y^{2}}{5} = 1$

Vedclass · Answer

(A) The vertices are $(\pm 2, 0)$,which lie on the $x$-axis. Thus,the equation of the hyperbola is of the form $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$. Given vertices $(\pm a, 0) = (\pm 2, 0)$,we have $a = 2$,so $a^{2} = 4$. Given foci $(\pm c, 0) = (\pm 3, 0)$,we have $c = 3$,so $c^{2} = 9$. For a hyperbola,we know the relation $c^{2} = a^{2} + b^{2}$. Substituting the values,$9 = 4 + b^{2}$,which gives $b^{2} = 5$. Therefore,the equation of the hyperbola is $\frac{x^{2}}{4} - \frac{y^{2}}{5} = 1$.

Find the equation of the hyperbola satisfying the given conditions: Vertices $(\pm 2, 0)$,foci $(\pm 3, 0)$.

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