Question

g find parametric equations of an ellipse cetnered at the originw ith major axis of length 18 on the x axis and minor axis oof length 12 on the yaxis, generated ccoutnerclockwise. graphj the ellipse and find a description in terms off x and y

Answer 1

Explanation:

The description in terms of x and y when 0 ≤ t ≤ 2π can be computed as follows.

From the given information:

The major axis 2a = 18

a = 18/2

a = 9

i.e (0, ± 9)

On the minor axis; 2b = 12

b = 12/2

b = 6

(±6, 0)

The graph of the ellipse is displayed in the diagram below.

The description in term of x and y is:

`(x^2)/(6^2)+ (y^2)/(9^2) = 1 \\ \\ \\ \text{from the graph} \\ \\ x = 6 cos t \ \ \ y = 9 sin t \ \ \ \ \ where (0\le t \le 2 \pi)`