Trigonometry hardest questions

Question

 x^2/a^2 + y^2/b^2 = 2
know have to squar them... but really confused....
pleasee help mee...????

Answer 1

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

(x-h)²/a² + (y-k)²/b² = 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.

Answer 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.