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Rewrite to standard form by completing the square and identify the conic: a) x² +16y² - 10x +96y + 153 = 0 = 0 b) 4x² 25y²8x100y-196 c) y² + 6x8y - 31 = 0

Rewrite to standard form by completing the square and identify the conic: a) x² +16y² - 10x +96y + 153 = 0 = 0 b) 4x² 25y²8x100y-196 c) y² + 6x8y - 31 = 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Conic Sections: Completing the Square To rewrite the given equations in standard form by completing the square, follow these steps for each equation. Identify the type of conic section (ellipse, hyperbola, parabola, or circle) each equation represents. #### a) \( x^2 + 16y^2 - 10x + 96y + 153 = 0 \) #### b) \( 4x^2 - 25y^2 - 8x - 100y - 196 = 0 \) #### c) \( y^2 + 6x - 8y - 31 = 0 \) To solve these, we'll go through the process of completing the square for the terms involving \(x\) and \(y\) in each equation. This will help us rewrite them in a more recognizable standard form to identify the conic section they represent.
Transcribed Image Text:### Conic Sections: Completing the Square To rewrite the given equations in standard form by completing the square, follow these steps for each equation. Identify the type of conic section (ellipse, hyperbola, parabola, or circle) each equation represents. #### a) \( x^2 + 16y^2 - 10x + 96y + 153 = 0 \) #### b) \( 4x^2 - 25y^2 - 8x - 100y - 196 = 0 \) #### c) \( y^2 + 6x - 8y - 31 = 0 \) To solve these, we'll go through the process of completing the square for the terms involving \(x\) and \(y\) in each equation. This will help us rewrite them in a more recognizable standard form to identify the conic section they represent.
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