{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Engineering Calculus Notes 154

Engineering Calculus Notes 154 - 142 CHAPTER 2 CURVES gives...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
142 CHAPTER 2. CURVES gives a curve satisfying x 2 a 2 y 2 b 2 = 1 . However, note that cosh t is always positive (in fact, cosh t 1 for all t ), so this parametrizes only the “right branch” of the hyperbola; the “left branch” is parametrized by −→ p ( t ) = ( a cosh t,b sinh t ) −∞ <t< . Similarly, the two branches of x 2 a 2 y 2 b 2 = 1 are parametrized by −→ p ( t ) = ( a sinh t, ± b cosh t ) −∞ <t< . Parabolas: The model equation for a parabola with horizontal directrix (Equation ( 2.10 ) in § 2.1 ) y = ax 2 is easily parametrized using x as the parameter: x = t y = at 2 which leads to −→
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern