Explanation Given: The given equation for hyperbola is, 16 x 2 − y 2 = 25 Approach: The general formula for hyperbola equation, A x 2 − B y 2 = C Here, C is constant term. To find the x -intercept, Substitute 0 for y in the general equation of hyperbola and solve for x as follows, A x 2 − B ( 0 ) 2 = C To find y -intercepts, Substitute 0 for x in the general equation of hyperbola and solve for y as follows, A ( 0 ) 2 − B y 2 = C To find the equation for the asymptotes replace the constant term of A x 2 − B y 2 = C with 0 and solve for y as follows, A x 2 − B y 2 = 0 Calculation: Consider the hyperbola equation, 16 x 2 − y 2 = 25 → ( 1 ) Compare above equation with general equation A x 2 − B y 2 = C . The value of A is 16 , B is 1 and C is 25 . Calculate the x -intercepts, Substitute 0 for y in equation ( 1 ) . 16 x 2 − ( 0 ) 2 = 25 x 2 = 25 16 x = ± 5 4 Thus the x -intercepts of the hyperbola are ( 5 4 , 0 ) and ( 0 , − 5 4 )

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ISBN: 9781285195728

Author: Jerome E. Kaufmann, Karen L. Schwitters

Publisher: Cengage Learning

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Chapter 8.4, Problem 2PS

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The intercepts and the equation of the asymptotes for the given hyperbola

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A copier was purchased for $16,200. For tax purposes the machine depreciates at $1800 per year. If x represents the number of years after the purchase, then the value of the copier (y) after x years is given by the equation y = 16,200 – 1800x. Find the x- and y-intercepts and explain the significance of each intercept. Also find the value of the copier after 6 years. What is the y-intercept? (Type an ordered pair.) Choose the statement that best describes the significance of the y-intercept. A. The copy machine is worth $16,200 less than it was worth when it was new. B. Each year the copy machine is worth $16,200 less than it was worth the year before. O C. The original value of the copy machine is $16,200. D. The value of the copy machine is never less than $16,200 What is the x-intercept? (Type an ordered pair.) Choose the statement that best describes the significance of the x-intercept. A. The copy machine has no value after 9 years. O B. The copy machine is worth $9 after 9 years.…

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Intermediate Algebra

Ch. 8.1 - For Problems 110, answer true or false. The graph...Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Prob. 4CQ Ch. 8.1 - Prob. 5CQ Ch. 8.1 - Prob. 6CQ Ch. 8.1 - Prob. 7CQ Ch. 8.1 - Prob. 8CQ Ch. 8.1 - Prob. 9CQ Ch. 8.1 - Prob. 10CQ

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The intercepts and the equation of the asymptotes for the given hyperbola

Solution Summary: The author explains how to find the intercepts and the equation of the asymptotes for the given hyperbola equation.

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To find: The intercepts and the equation of the asymptotes for the given hyperbola

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Chapter 8 Solutions

To find:

The intercepts and the equation of the asymptotes for the given hyperbola