Calculus Homework

Question

Consider . Given , Which of the followin statements about the level curve is correct?

The level curve is 

None of these.

The level curve is 

     .

The level curve is       .

      .

which of the following statements about the level curve is correct:which of the following statements about the level curve is correct:  , which of the following statements about the level curve is correct:          .

Answer 1

The level curve is the set of points (x, y) satisfying

2x² + 2y² = 1

Rewriting

y² = 0.5 - x²

When x∈(-√0.5, √0.5) then y²>0 and therefore y is real and can be both positive and negative.

Therefore the answer of the last one

y = ±√(0.5 - x²)