The values of a and b in the parametric equations x = a cos t and y = b sin t determine the shape of the conic section that will be traced.
1. If a = b, the conic section traced will be a circle. This is because the parametric equations x = a cos t and y = b sin t reduce to x = a cos t and y = a sin t, which are the parametric equations for a circle.
2. If a is not equal to b, the conic section traced will be an ellipse. The eccentricity of the ellipse will be determined by the ratio of a to b. If a is greater than b, the ellipse will be elongated along the x-axis, while if b is greater than a, the ellipse will be elongated along the y-axis.
3. If a = 0 or b = 0, the conic section traced will be a straight line. If a = 0, the line will be parallel to the y-axis, while if b = 0, the line will be parallel to the x-axis.
In summary, the values of a and b in the parametric equations x = a cos t and y = b sin t determine whether the conic section traced will be a circle, ellipse, or straight line, and the specific shape of the conic section will depend on the relationship between a and b.
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.
1 answer