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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285741550

Chapter 10.5, Problem 28E

Textbook Problem

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Identify the type of conic section whose equation is given and find the vertices and foci.

**28.** *y*^{2} − 2 = *x*^{2} − 2*x*

To determine

**To identify:** The type of conic section from the equation

**Formula used:**

The hyperbola

**Calculation:**

The given equation is,

Rewrite the equation as follows.

This equation represents a hyperbola.

Compute the center of the hyperbola using the equation.

Therefore, the center of the hyperbola

Calculus: Early Transcendentals

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Then find the...Ch. 10.5 - Find an equation of the parabola. Then find the...Ch. 10.5 - Find the vertices and foci of the ellipse and...Ch. 10.5 - Find the vertices and foci of the ellipse and...Ch. 10.5 - Find the vertices and foci of the ellipse and...Ch. 10.5 - Find the vertices and foci of the ellipse and...Ch. 10.5 - Find the vertices and foci of the ellipse and...Ch. 10.5 - Find the vertices and foci of the ellipse and...Ch. 10.5 - Find an equation of the ell ipse. Then find its...Ch. 10.5 - Find an equation of the ell ipse. 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(b)...Ch. 10 - (a) Give a definition of an ellipse in terms of...Ch. 10 - (a) Give a definition of a hyperbola in terms of...Ch. 10 - (a) What is the eccentricity of a conic section?...Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Determine whether the statement is true or false....Ch. 10 - Sketch the parametric curve and eliminate the...Ch. 10 - Sketch the parametric curve and eliminate the...Ch. 10 - Sketch the parametric curve and eliminate the...Ch. 10 - Sketch the parametric curve and eliminate the...Ch. 10 - Write three different sets of parametric equations...Ch. 10 - Use the graphs of x = f(t) and y = g(t) to sketch...Ch. 10 - (a) Plot the point with polar coordinates (4,...Ch. 10 - Sketch the region consisting of points whose polar...Ch. 10 - Sketch the polar curve. 9. r = 1 + sinCh. 10 - Sketch the polar curve. 10. r = sin 4Ch. 10 - Sketch the polar curve. 11. r = cos 3Ch. 10 - Sketch the polar curve. 12. r = 3 + cos 3Ch. 10 - Sketch the polar curve. 13. r = 1 + cos 2Ch. 10 - Sketch the polar curve. 14. r = 2 cos(/2)Ch. 10 - Sketch the polar curve. 15. r=31+2sinCh. 10 - Sketch the polar curve. 16. r=322cosCh. 10 - Find a polar equation for the curve represented by...Ch. 10 - Find a polar equation for the curve represented by...Ch. 10 - The curve with polar equation r = (sin )/ is...Ch. 10 - Graph the ellipse r = 2/(4 3 cos ) and its...Ch. 10 - Find the slope of the tangent line to the given...Ch. 10 - Find the slope of the tangent line to the given...Ch. 10 - Find the slope of the tangent line to the given...Ch. 10 - Find the slope of the tangent line to the given...Ch. 10 - Find dy/dx and d2y/dx2. 25. x = t + sin t, y = t ...Ch. 10 - Find dy/dx and d2y/dx2. 26. x = 1 + t2, y = t t3Ch. 10 - Use a graph to estimate the coordinates of the...Ch. 10 - Find the area enclosed by the loop of the curve in...Ch. 10 - At what points does the curve x = 2a cos t a cos...Ch. 10 - Find the area enclosed by the curve in Exercise...Ch. 10 - Find the area enclosed by the curve r2 = 9 cos 5.Ch. 10 - Find the area enclosed by the inner loop of the...Ch. 10 - Find the points of intersection of the curves r =...Ch. 10 - Find the points of intersection of the curves r =...Ch. 10 - Find the area of the region that lies inside both...Ch. 10 - Find the area of the region that lies inside the...Ch. 10 - Find the length of the curve. 37. x = 3t2, y =...Ch. 10 - Find the length of the curve. 38. x = 2 + 3t, y =...Ch. 10 - Find the length of the curve. 39. r = 1/, 2Ch. 10 - Find the length of the curve. 40. r = sin3(/3), 0Ch. 10 - Find the area of the surface obtained by rotating...Ch. 10 - Find the area of the surface obtained by rotating...Ch. 10 - The curves defined by the parametric equations...Ch. 10 - A family of curves has polar equations ra = | sin...Ch. 10 - Find the foci and vertices and sketch the graph....Ch. 10 - Find the foci and vertices and sketch the graph....Ch. 10 - Find the foci and vertices and sketch the graph....Ch. 10 - Find the foci and vertices and sketch the graph....Ch. 10 - Find an equation of the ellipse with foci (4, 0)...Ch. 10 - Find an equation of the parabola with focus (2, 1)...Ch. 10 - Find an equation of the hyperbola with foci (0, ...Ch. 10 - Find an equation of the ellipse with foci (3, 2)...Ch. 10 - Find an equation for the ellipse that shares a...Ch. 10 - Show that if m is any real number, then there are...Ch. 10 - Find a polar equation for the ellipse with focus...Ch. 10 - Show that the angles between the polar axis and...Ch. 10 - In the figure the circle of radius a is...Ch. 10 - A curve called the folium of Descartes is defined...Ch. 10 - The outer circle in the figure has radius 1 and...Ch. 10 - (a) Find the highest and lowest points on the...Ch. 10 - What is the smallest viewing rectangle that...Ch. 10 - Four bugs are placed at the four corners of a...Ch. 10 - Show that any tangent line to a hyperbola touches...Ch. 10 - A circle C of radius 2r has its center at the...

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Calculus: An Applied Approach (MindTap Course List)

Evaluate the iterated integral. 5. 010s2cos(s3)dtds

Multivariable Calculus

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Applied Calculus

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. y2x[2...

Finite Mathematics and Applied Calculus (MindTap Course List)

A researcher studies the factors that determine the number of jobs adults have in a lifetime. The variable, num...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Per capita expenditures for public transportation for 20 cities are reported here for 2000 and 2010. Compute th...

Essentials Of Statistics

918 Evaluate the triple integral. EydV, where E={(x,y,z)0x3,0yx,xyzx+y}

Calculus (MindTap Course List)

16. Explain why honesty is a hypothetical construct instead of a concrete variable. Describe how shyness might ...

Statistics for The Behavioral Sciences (MindTap Course List)

The graph of y=3xx2 is given. Use transformations to create a function whose graph is as shown. 6.

Single Variable Calculus

Poiseuilles Law According to a law discovered by the nineteenth century physician Poiseuille. The velocity (in ...

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

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. y2x[2...

Finite Mathematics

A family decides to have children until it has three children of the same gender. Assuming P(B) = P(G) = .5, wh...

Probability and Statistics for Engineering and the Sciences

Critical Thinking A consumer interest group is tracking the percentage of household income spent on gasoline ov...

Understanding Basic Statistics

In Exercises 41 to 50, use deduction to state a conclusion, if possible. All mathematics teachers have a strang...

Elementary Geometry For College Students, 7e

For Problems 56-64, use your calculator to evaluate each numerical expression. Objective 3 (3.14)3

Intermediate Algebra

Subtract the following mixed numbers and reduce to lowest terms. 634423 b. 25291156

Contemporary Mathematics for Business & Consumers

In Problems 5-8, assume that x and y are differentiable functions of t. In each case, find given that .
7.

Mathematical Applications for the Management, Life, and Social Sciences

Use the given nth-term formula to compute the first five terms of the sequence. an=5n23n

Mathematical Excursions (MindTap Course List)

Factor completely. Check by multiplying the factors: m21

Elementary Technical Mathematics

Solving an Inequality In Exercises 119-122, solve the inequality for x. e1x6

Calculus: Early Transcendental Functions (MindTap Course List)

Length A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (3, 2...

Calculus of a Single Variable

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in whic...

Single Variable Calculus: Early Transcendentals

41. Prove or disprove that the set in Exercise is a group with respect to addition.
39. Let be the set of a...

Elements Of Modern Algebra

Multiply. Leave all answers in trigonometric form. 2cis344cis4

Trigonometry (MindTap Course List)

Find the curl of F(x, y, z) = (x2 + y2)i + (xz)j + (yz)k.
−zi + 2yj + xk
(z − x)i + (z − 2y)k
(x − z)i + 2xj + ...

Study Guide for Stewart's Multivariable Calculus, 8th

Suppose in an estimation of a root of f(x) = 0 we make an initial guess x1 and it turns out that f'′(x1) = 0. W...

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

Refer to the circle with centre P. a Use a protractor to find m1. b Use a protractor to find m2. c Compare resu...

Elementary Geometry for College Students

In Exercises 1-22, evaluate the given expression. C(7,5)

Finite Mathematics for the Managerial, Life, and Social Sciences

Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the curve C in ...

Multivariable Calculus

Normals to a Parabola The graph shows die normal lines from the point (2.0) to the graph of the parabola x=y2. ...

Calculus (MindTap Course List)

Express the following ratios in lowest fractional form. 9. 2:11

Mathematics For Machine Technology

Consider the following data for two variables, x and y. x 9 32 18 15 26 y 10 20 21 16 22 a. Develop an estimate...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

You have discovered that when you are in a hurry, you can save time by rolling through stop signs instead of co...

Research Methods for the Behavioral Sciences (MindTap Course List)

Suppose that you were asked to help design a survey of adult city residents in order to estimate the proportion...

Introduction To Statistics And Data Analysis

Explain why partial counterbalancing is sometimes necessary.

Research Methods for the Behavioral Sciences (MindTap Course List)

According to a survey conducted by TD Ameritrade, one out of four investors have exchange-traded funds in their...

Statistics for Business & Economics, Revised (MindTap Course List)

Write each expression without absolute value symbols. |x5| and x5

College Algebra (MindTap Course List)