Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.
Vertices: ; foci:

Question

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. ​
Vertices:  ; foci:  ​

Quizplus · Accepted Answer

The distance between the center and vertices is given by $a$, and the distance between the center and foci is given by $c$. Since the center is at the origin, we can use the standard form of the hyperbola, which is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. We know that the hyperbola has horizontal transverse axis since the distance between the center and vertices is greater than the distance between the center and foci. Thus, we have $a>c$ and $b^2=a^2-c^2$. Using the distance formula, we have $a=\frac{11}{2}$ and $c=\frac{1}{2}$. Substituting in gives us $\frac{x^2}{(\frac{11}{2})^2}-\frac{y^2}{(\frac{5\sqrt{15}}{2})^2}=1$, which simplifies to $\boxed{	extbf{(C)}\ 11eacce6\_20cf\_1cd1\_9f49\_11f71277d64e\_TB7896\_11}$.

Find the Standard Form of the Equation of the Hyperbola