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 8 x + 31 − x y = y ( y − 2 − x ) as, 8 x + 31 − x y = y 2 − 2 y − x y y 2 − 8 x − 2 y − 31 = 0 Note that, y 2 − 8 x − 2 y − 31 = 0 is of the form A x 2 + B x y + C y 2 + D x + E y + F = 0 where A = 0 , B = 0 , C = 1 , D = − 8 , E = − 2 , F = − 31 . It can be observed that A = 0 , C = 1 and B = 0 . From the above definition, it can be concluded that the equation 8 x + 31 − x y = y ( y − 2 − x ) represents a parabola. Thus, the type of curve represented by the equation 8 x + 31 − x y = y ( y − 2 − x ) is a parabola _

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn 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 36E

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The type of curve represented by the equation 8x+31−xy=y(y−2−x) and sketch the curve using a calculator.

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Chapter 21.8, Problem 35E

Chapter 21.8, Problem 37E

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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 8 x + 31 − x y = y ( y − 2 − x ) and sketch the curve using a calculator.

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The type of curve represented by the equation 8x+31−xy=y(y−2−x) and sketch the curve using a calculator.

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