Explanation Definition used: Identifying a Conic Section from the Second-degree Equation: The second degree equation is of the form A x 2 + B x y + C y 2 + D x + E y + F = 0 . 1. If A = C , B = 0 , a circle . 2. If A ≠ C ( Same sign ) , B = 0 , an ellipse . 3. If A and C have different signs , B = 0 , a hyperbola . 4. If A = 0 , C = 0 , B ≠ 0 , a hyperbola . 5. If either A = 0 or C = 0 ( both not both ) , B = 0 , a parabola . Calculation: Note that, 4 y 2 − x 2 + 40 y − 4 x + 60 = 0 is of the form A x 2 + B x y + C y 2 + D x + E y + F = 0 where A = − 1 , B = 0 , C = 4 , D = − 4 , E = 40 , F = 60 . It can be observed that A = − 1 , C = 4 and B = 0 where A and C have different signs. From the above definition, it can be concluded that the equation 4 y 2 − x 2 + 40 y − 4 x + 60 = 0 represents a hyperbola. Thus, the type of curve represented by the equation 4 y 2 − x 2 + 40 y − 4 x + 60 = 0 is a hyperbola _

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 21.8, Problem 32E

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The type of curve represented by the equation 4y2−x2+40y−4x+60=0 and sketch the curve using a calculator.

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Chapter 21.8, Problem 31E

Chapter 21.8, Problem 33E

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Chapter 21 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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The type of curve represented by the equation 4 y 2 − x 2 + 40 y − 4 x + 60 = 0 and sketch the curve using a calculator.

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The type of curve represented by the equation 4y2−x2+40y−4x+60=0 and sketch the curve using a calculator.

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Chapter 21 Solutions