Question

R=4/1+3cosθ Find the eccentricity and identify the conic.

Answer 1

The equation represents an ellipse with a given eccentricity.

Step-by-step explanation:

To find the eccentricity and identify the conic, we need to rewrite the equation in standard form. First, rewrite the equation by multiplying the numerator and denominator by 1-3cosθ:

r = (4/1+3cosθ)(1-3cosθ) = (4-12cosθ + 9cos²θ) / (1+3cosθ)

Now, simplify the equation:

r = (9cos²θ - 12cosθ + 4)/(1 + 3cosθ)

This equation represents an ellipse, as it is in the form of (x/a)² + (y/b)² = 1, with a = 1/(1+3cosθ) and b = 1/(3cosθ - 3).