Question

44.
The product of inertia of an elliptic quadrant about its area
(a) ma 26^2/2.11
(b) mab 21
(c) ma 36^3/21
(d)ma 4b^4 20​

Answer 1

The first step involves determining the parametric equation of an ellipse.

It is given as;

(a cos t, b sin t)

Now we need to modify the parametric equation to get the transformation equation. We get;

(r cos θ, λ r sin θ)

Where

λ= b / a

Here, we have to consider a and b as the semi-major and semi-minor axis of the ellipse.

a = semi-major axis

b = semi-minor axis

We get the transformation equation as;

x = r cos θ

y = λ r sin⁡ θ