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

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In summary, the conversation discusses solving the equation y^2= 1- 2x^2 to find the foci and other properties of the ellipse. The next step is to compare this equation with the general equation for an ellipse, x^2/a^2 + y^2/b^2 = 1, and determine the values of a and b that will result in the same set of solutions. This can be done by equating 2x^2 with x^2/a^2 and y^2 with y^2/b^2 and solving for a and b. The position of the loci can then be derived from these values.
  • #1
wat2000
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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?
 
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  • #2
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?
 
  • #3
should I put everything over 1? so that the 1 stays the same?
 
  • #4
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).
 

1. What is the equation for finding the foci of a quadratic?

The equation for finding the foci of a quadratic is y2 = 1 - 2x2.

2. How do you identify the foci of a quadratic?

The foci of a quadratic can be identified by using the formula (±√(a2-b2),0) where a2 is the coefficient of x2 and b2 is the coefficient of y2.

3. Can the foci of a quadratic be imaginary numbers?

Yes, the foci of a quadratic can be imaginary numbers if the value inside the square root in the formula is negative. This indicates that the quadratic does not have any real roots.

4. How many foci can a quadratic have?

A quadratic can have either two foci or no foci. If the value inside the square root in the formula is positive, there will be two real foci. If it is negative, there will be no real foci.

5. Can the foci of a quadratic lie outside of the curve?

No, the foci of a quadratic will always lie on the curve or inside the curve. If the foci lie outside of the curve, it indicates an incorrect equation or calculation.

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