Algebra/Chapter 17/Hyperbolas

Algebra

Hyperbolas can be thought of as the "opposite" of ellipses - instead of the sum of distances from two foci, the difference is used. This leads to two curves that point in opposite directions. The major axis is 2a units long, and the transverse axis is 2b units long. When a² + b² = c², eccentricity is again c/a. The foci are at either side of the major axis, c units away from the center.

An "east-west" hyperbola is written as:

${\frac {\left(x-h\right)^{2}}{a^{2}}}-{\frac {\left(y-k\right)^{2}}{b^{2}}}=1$

while a "north-south" one is written as:

${\frac {\left(y-k\right)^{2}}{a^{2}}}-{\frac {\left(x-h\right)^{2}}{b^{2}}}=1$

For rectangular hyperbolas with the coordinate axes parallel to their asymptotes:

As the curve progresses, it gets closer and closer to two lines called asymptotes. In the second image, the asymptotes are y = ±x. The length of each latus rectum is (..?)