Question

Which of the following represents the polar equation r = (tan²θ)(cscθ) as a rectangular equation?

1) (x² + y²)² = x² - y²
2) (x² + y²)² = x² + y²
3) (x² + y²)² = x² + 2y²
4) (x² + y²)² = x² - 2y²

Answer 1

Option 3, (x² + y²)² = x² + 2y², represents the given polar equation as a rectangular equation.

Step-by-step explanation:

The polar equation r = (tan²θ)(cscθ) can be represented as a rectangular equation using the relationship between polar and rectangular coordinates. In rectangular coordinates, the equation becomes (x² + y²)² = x² + 2y². Option 3, (x² = x² + 2y²+ y²)² , represents the given polar equation as a rectangular equation.