Explanation Given: ( x + c ) 2 + y 2 − ( x − c ) 2 + y 2 = ± 2 a Approach: Take the second term to the right side then squaring both sides. After that, some rearrangement, and we will get the desired result. Calculation: ( x + c ) 2 + y 2 − ( x − c ) 2 + y 2 = ± 2 a ( x + c ) 2 + y 2 = ± 2 a + ( x − c ) 2 + y 2 Now, squaring both sides, we get ( x + c ) 2 + y 2 = 4 a 2 + ( x − c ) 2 + y 2 ± 4 a ( x − c ) 2 + y 2 x 2 + c 2 + 2 c x = 4 a 2 + x 2 + c 2 − 2 c x ± 4 a ( x − c )

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 12.3, Problem 53E

To determine

To find:

The steps needed to show in the derivation of the equation of the hyperbola which says the equation

(x+c)2+y2−(x−c)2+y2=±2a

simplifies to

(c2−a2)x2−a2y2=a2(c2−a2)

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Chapter 12.3, Problem 52E

Chapter 12.3, Problem 54E

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Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

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The steps needed to show in the derivation of the equation of the hyperbola which says the equation ( x + c ) 2 + y 2 − ( x − c ) 2 + y 2 = ± 2 a simplifies to ( c 2 − a 2 ) x 2 − a 2 y 2 = a 2 ( c 2 − a 2 )

Solution Summary: The author explains how the equation sqrt(x+c)2+y 2=pm 2a simplifies.

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To find:

The steps needed to show in the derivation of the equation of the hyperbola which says the equation

(x+c)2+y2−(x−c)2+y2=±2a

simplifies to

(c2−a2)x2−a2y2=a2(c2−a2)

Want to see the full answer?

Chapter 12 Solutions

The steps needed to show in the derivation of the equation of the hyperbola which says the equation ( x + c ) 2 + y 2 − ( x − c ) 2 + y 2 = ± 2 a simplifies to ( c 2 − a 2 ) x 2 − a 2 y 2 = a 2 ( c 2 − a 2 )

Solution Summary: The author explains how the equation sqrt(x+c)2+y 2=pm 2a simplifies.

Videos

To find: The steps needed to show in the derivation of the equation of the hyperbola which says the equation (x+c)2+y2−(x−c)2+y2=±2a simplifies to (c2−a2)x2−a2y2=a2(c2−a2)

Want to see the full answer?

Chapter 12 Solutions

To find:

The steps needed to show in the derivation of the equation of the hyperbola which says the equation

(x+c)2+y2−(x−c)2+y2=±2a

simplifies to

(c2−a2)x2−a2y2=a2(c2−a2)