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. im 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?
Try match the equation for your particular ellipse, 2x^{2} + y^{2} = 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?
I think you misunderstand. If you compare the equation 2x^{2} + y^{2} = 1 with x^{2}/a^{2} + y^{2}/b^{2} = 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: 2x^{2} must be equal to x^{2}/a^{2} for all x, and likewise y^{2} must equal y^{2}/b^{2} 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 text book on how this position is related to the value of a and b).