   Chapter 10.5, Problem 28E

Chapter
Section
Textbook Problem

Identify the type of conic section whose equation is given and find the vertices and foci.28. y2 − 2 = x2 − 2x

To determine

To Find: The type of conic section, vertices, and foci for the equation y22=x22x .

Explanation

Given:

The equation is as follows.

y22=x22x (1)

Rewrite the equation.

y2x2+2x+1=21

Factorize the above equation as below.

y2(x1)2=1

Divide the above equation by (1).

y21(x1)21=11

y21(x1)21=1 (2)

Then, compare the equation (2) with the standard equation of hyperbola.

y2a2x2b2=1 (3)

Therefore, the type of conic section is hyperbola_ .

Calculation:

Compute the center of the hyperbola using the equation.

(yk)2a2+(xh)2b2=1(y0)21+(x(1))21=1

Therefore, the center of the hyperbola (h,k) is (0,1) .

Substitute the value 1 for a2 and 1 for b2 in equation (3).

a2=1a=1

b2=1b=1

Compute the vertices

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 1-6, simplify the expression. 2. 2a23ab9b22ab2+3b3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Find each product. a(4x26y+1)

Elementary Technical Mathematics

The distance between (7, 4, –3) and (–1, 2, 3) is: 4 16 104

Study Guide for Stewart's Multivariable Calculus, 8th

limx0cscx= a) 0 b) c) d) does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 