(a) Show that the right and left branches of the hyperbolax2a2 y2b2 = 1can be

Chapter 10, Problem 36

(choose chapter or problem)

(a) Show that the right and left branches of the hyperbola

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

can be represented parametrically as

$x=a \cosh t, y=b \sinh t(-\infty<t<+\infty) x=-a \cosh t, y=b \sinh t(-\infty<t<+\infty)$

(b) Use a graphing utility to generate both branches of the hyperbola $x^{2}-y^{2}=1$ on the same screen.

Equation Transcription:

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

$x=a\ cosh\ t,\ y=b\ sinh\ t\ (-\infty{}<t<+\infty{})x=-a\ cosh\ t,\ y=b\ sinh\ t(-\infty{}<t<+\infty{})$

${x}^{2}-{y}^{2}=1$

Text Transcription:

x^2 /a^2 -y^2 /b^2 =1

x=a cosh t, y=b sinh t(-infinity <t<+infinity)x=-a cosh t, y=b sinh t(-infinity<t<+infinity)

x^2 -y^2 =1

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Login