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: Rewrite x 2 − 4 y = y 2 + 4 ( 1 − x ) as, x 2 − 4 y = y 2 + 4 − 4 x x 2 − y 2 + 4 x − 4 y − 4 = 0 Note that, x 2 − y 2 + 4 x − 4 y − 4 = 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 = − 1 , D = 4 , E = − 4 , F = − 4 . It can be observed that A = 1 , C = − 1 and B = 0 . From the above definition, it can be concluded that the equation x 2 − 4 y = y 2 + 4 ( 1 − x ) represents a hyperbola. Thus, the type of curve represented by the equation x 2 − 4 y = y 2 + 4 ( 1 − x ) is hyperbola _ . Rewrite x 2 − y 2 + 4 x − 4 y − 4 = 0 as, x 2 − y 2 + 4 x − 4 y − 4 = 0 x 2 + 4 x + 4 − ( y 2 + 4 y + 4 ) = 4 ( x + 2 ) 2 − ( y + 2 ) 2 = 4 ( x + 2 ) 2 4 −<

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ISBN: 9780134437705

Author: Washington

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 30E

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The type of curve represented by the equation x2−4y=y2+4(1−x) and sketch the curve.

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Chapter 21.8, Problem 29E

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Chapter 21 Solutions

Basic Technical Mathematics

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 x 2 − 4 y = y 2 + 4 ( 1 − x ) and sketch the curve.

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