To determine: The conic section and to find the vertices and foci: x2 - y2y=4

Anonym 2020-12-24 Answered

To determine: The conic section and to find the vertices and foci: x2  y2y=4

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hajavaF
Answered 2020-12-25 Author has 90 answers

The equation x2  2y2=4 can be written as: x2  2y2=4x24  2y24=2(x2)2  (y2)2=1 The standard equation of hyperbola with foci (± c, 0) will be given by: (xa)2  (yb)2=1 Thus, on comparing equations x2  2y2=4x24  2y24=2(x2)2  (y2)2=1 and (xa)2  (yb)2=1 we find that the given conic is a hyperbola. Now, compare equation x2  2y2=4x24  2y24=2(x2)2  (y2)2=1 and (xa)2  (yb)2=1 and we get: a=2 and b=2 Now, c=a2 + b2=4 + 2=6 Thus, the vertices of the given conic are (± 2, 0) The foci of the given conic is (± 6, 0) Conclusion: Hence, the given conic section is a hyperbola. The vertices of hyperbola are (± 2, 0) and the foci of the hyperbola is (± 6, 0).

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