(a) Find parametric equations for the ellipse x^2 / a^2+y^2 / b^2=1. [Hint: Modify the equations

Name: (a) Find parametric equations for the ellipse x^2 / a^2+y^2 / b^2=1. [Hint: Modify the equations of the circle in Example 2.] (b) Use these parametric equations to graph the ellipse when a=3 and b=1,2,4, and 8 . (c) How does the shape of the ellipse change as b varies?
Uploaded: 2022-03-20T17:48:47-08:00
Duration: 35 s
Channel: Krishna G
Description: (a) Find parametric equations for the ellipse x^2 / a^2+y^2 / b^2=1. [Hint: Modify the equations of the circle in Example 2.] (b) Use these parametric equations to graph the ellipse when a=3 and b=1,2,4, and 8 . (c) How does the shape of the ellipse change as b varies?

Question

Krishna G · Accepted Answer

Step 1:**  
The parametric equations for the ellipse $x^{2}/a^{2} + y^{2}/b^{2} = 1$ are:
[ x =

Question

(a) Find parametric equations for the ellipse $x^{2} / a^{2}+y^{2} / b^{2}=1$. [Hint: Modify the equations of the circle in Example 2.] (b) Use these parametric equations to graph the ellipse when $a=3$ and $b=1,2,4$, and 8 . (c) How does the shape of the ellipse change as $b$ varies?

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