Finding the Foci of a Quadratic: Working with y^2=1-2x^2

[wat2000]

y^2= 1- 2x^2

im supposed to put it in x^2/a^2 + y^2/b^2 = 1 to find the foci and so forth.

when i try to set it up i get 2x^2 + y^2 = 1. I am not sure where to go from here. if i multiply or divide to set the problem up properly the 1 will change and my equation will be messed up. can someone show me what my next step is?

 

[Filip Larsen]

Try match the equation for your particular ellipse, 2x² + y² = 1, with the general equation for an ellipse which you have also written up. What value must a and b have in order to match your equation?

 

[wat2000]

should I put everything over 1? so that the 1 stays the same?

 

[Filip Larsen]

I think you misunderstand. If you compare the equation 2x² + y² = 1 with x²/a² + y²/b² = 1, then what value must a and b have for the two equations to have the same set of solutions, that is, for them to express the same ellipse?

Hint: 2x² must be equal to x²/a² for all x, and likewise y² must equal y²/b² for all y. Solving these two equations will to get you a and b, and from these you should be able to derive the position of the loci (you may want to look in your textbook on how this position is related to the value of a and b).