• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q. 40

Found in: Page 725


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.


Short Answer

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38–43.

foci (0,±4), directrices y=±1

The equation is y24-x212=1.

See the step by step solution

Step by Step Solution

Step 1. Given information.

We are given,

foci (0,±4), directrices y=±1

Step 2. Value of the variables.

Now, as given,

The focus points are (0,4),(0,-4). Center =0+02,4-42 since mid point =x1+x22,y1+y22 Center =(0,0) Given directries are y=±1. That means be=1b=e Then be=4b·b=4[ since e=b]b2=4c=(0-4)2+(0-0)2 since D=x2-x12+y2-y12 That is the distance from (0,4)(0,0)c=4 For a hyperbola, a2+b2=c2a2+4=42a2=12

Step 3. Substitution.

Now, substitute the obtained values,

(y-k)2b2-(x-h)2a2=1 where (h,k) is the center. (y-0)24-(x-0)212=1 since a2=12,b2=4y24-x212=1

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.