SOLUTION: x^2/a^2+y^2/a^2-(2xy/a^2)cos45=sin^2(45) please tell me what is the graphical shape of this equation.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: x^2/a^2+y^2/a^2-(2xy/a^2)cos45=sin^2(45) please tell me what is the graphical shape of this equation.      Log On


   

Question 249588: x^2/a^2+y^2/a^2-(2xy/a^2)cos45=sin^2(45)
please tell me what is the graphical shape of this equation.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

The general equation of a conic section is:

Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0

The discriminant B%5E2-4AC is used to determine which 
conic section will result. 

1. If the discriminant is less than zero we have 
   (a). a circle if B = 0 and A = C, or 
   (b). an ellipse otherwise.
2. If the discriminant is equal to zero we have a parabola.
3. If the discriminant is greater than zero we have a hyperbola.


Your equation is:

x%5E2%2Fa%5E2%2By%5E2%2Fa%5E2-%282xy%2Fa%5E2%29Cos%28%2245%B0%22%29=Sin%5E2%28%2245%B0%22%29

We put the term in xy in between the terms in x%5E2%29%0D%0Aand+%7B%7B%7By%5E2, and get 0 on the right, so it will be in 
the same form as above:



we have  

A=1%2Fa%5E2,



C+=+1%2Fa%5E2

D=0,  E=0,  F=-Sin%5E2%28%2245%B0%22%29

So the discriminant = 

  

Since the discriminant is negative, by the rules at the
top we can conclude the equation represents an ellipse.

Edwin