Can someone please explain the last two questions of my homework please because I really don't get it.
Any help would be greatly appreciated!
Thanks in advance!
Set up a coordinate system so that the origin is at the center of the barbell, x-axis horizontal, y-axis vertical. The vertices of the hyperbola are at (-2, 0) and (2, 0). Further, the foci are at (-3, 0) and (3, 0) because the lie on vertical lines connecting the ends of radii of the hemispheres. For the hyperbola [tex]\frac{x^2}{a^2}- \frac{y^2}{b^2}= 1, the distance from the center to each focus is given by $\displaystyle f^2= a^2+ b^2$ so $\displaystyle 9= 4+ b^2$ and $\displaystyle b= \sqrt{5}$.
The equation of the hyperbola is $\displaystyle \frac{x^2}{4}- \frac{y^2}{5}= 1$.
At the ends of the hyperbolic section, x= 3 and -3, the same as for the foci which are on those lines. At those points $\displaystyle \frac{9}{4}- \frac{y^2}{5}= 1$. Solve for y. The length of the hyperbolic section is 2y because of the symmetry, and the entire length is that plus the two hemispheric radii: 2y+ 6.