Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q. 39

Expert-verified

Calculus

Found in: Page 772

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38–43.
$foci (\pm 6, 0), directrices x = \pm 1$

The equation is $\frac{x^{2}}{6} - \frac{y^{2}}{30} = 1 .$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given values are,

$foci (\pm 6, 0), directrices x = \pm 1$

Step 2. Value of variables.

Now,

$The focus points are (6, 0), (- 6, 0) . Center = (\frac{6 - 6}{2}, \frac{0 + 0}{2}) [since mid point = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})] Center = (0, 0) Given driectries are x = \pm 1 . a = e Then a e = 6 a^{2} = 6 c = \sqrt{(0 - 6)^{2} + (0 - 0)^{2}} [since D = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}] c = 6 For a hyperbola, a^{2} + b^{2} = c^{2} 6 + b^{2} = 6^{2} b^{2} = 30$

Step 3. Substitution.

Now, substitute the obtained values in,

$\frac{(x - h)^{2}}{a^{2}} - \frac{(y - k)^{2}}{b^{2}} = 1 where (h, k) is the center. \frac{(x - 0)^{2}}{6} - \frac{(y - 0)^{2}}{30} = 1 [since a^{2} = 6, b^{2} = 30] \frac{x^{2}}{6} - \frac{y^{2}}{30} = 1$

Most popular questions for Math Textbooks

Given two points in a plane, called _______, a hyperbola is the set of points in the plane for which ________.

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$directrix y = 0, focus (0, 1)$

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.

$x = 0$

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$r = \frac{α}{1 + \sin θ}$

Complete example 2 by evaluating the integral expression

$\int_{0}^{\frac{2 π}{3}} {(\frac{1}{2} + \cos θ)}^{2} d θ - \int_{π}^{\frac{4 π}{3}} {(\frac{1}{2} + \cos θ)}^{2} d θ$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free