Question

For parametric equations x= a cos t and y= b sin t, describe how the values of a and b determine which conic section will be traced.

Answer 1

Explanation:

x = a cos t, y = b sin t

cos t = x / a, sin t = y / b

cos² t + sin² t = 1

(x / a)² + (y / b)² = 1

If a = b, the conic section is a circle.

If a and b are different, the conic section is an ellipse.