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 4 x 2 + 4 = 9 − 8 x − 4 y 2 as, 4 x 2 + 4 − 9 + 8 x + 4 y 2 = 0 4 x 2 + 4 y 2 + 8 x − 5 = 0 Note that, 4 x 2 + 4 y 2 + 8 x − 5 = 0 is of the form A x 2 + B x y + C y 2 + D x + E y + F = 0 where A = 4 , B = 0 , C = 4 , D = 8 , E = 0 , F = − 5 . It can be observed that A = 4 , C = 4 and B = 0 . From the above definition, it can be concluded that the equation 4 x 2 + 4 = 9 − 8 x − 4 y 2 represents a circle. Thus, the type of curve represented by the equation 4 x 2 + 4 = 9 − 8 x − 4 y 2 is a circle _

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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 28E

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The type of curve represented by the equation 4x2+4=9−8x−4y2 and sketch the curve.

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The type of curve represented by the equation 4 x 2 + 4 = 9 − 8 x − 4 y 2 and sketch the curve.

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The type of curve represented by the equation 4x2+4=9−8x−4y2 and sketch the curve.

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