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Trigonometry hardest questions

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2 Answers

Not clear on what you are asking?!  The equation fits into the general formula for an ellipse,

(x-h)2/a2 + (y-k)2/b= 1

The length of the "major" (longer) axis of symmetry is "a"; the length of the "minor" (shorter) axis is "b"; there are two vertices and two co-vertices.  You can find all the details at

http://www.clausentech.com/lchs/dclausen/algebra2/ellipses.htm.

You can fit your formula into the general equation by dividing both sides by 2.

Square each to get x2/a2 cos2 Θ + xy/ab cos Θ sin Θ + y2/b2 sin 2 Θ = 1 and 
x2/a2 sin2 Θ - xy/ab cos Θ sin Θ + y2/b2 cos 2 Θ = 1. Now add them together - note that

1 - your center terms drop out 

2 - factor common terms and you will be left with
x2/a2 (cos2 Θ + sin 2Θ) + y2/b2 (cos2 Θ + sin 2Θ) = 2

3 - What does (cos2 Θ + sin 2Θ) equal? Replace it and solve.

Good luck. 

 

 

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