Define the equation of the given curve. Find the area of the enclosed region. Find the area when a = lo and b = 5.

Question

Using the given figure answer the following questions.

(i) Define the equation of the given curve.

(ii) Find the area of the enclosed region.

(iii) Find the area when a = 10 and b = 5.

Answer 1

(i) The figure represents an ellipse with equation

\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.\)

(ii) We have, \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.\)

⇒ y² = b² (1 - \(\frac{x^2}{a^2}\))

⇒ y = \(\frac{b}{a}\) \(\sqrt{a^2 -b^2}\)

Ellipse is symmetric w.r.t coordinate axles. Therefore the area of the enclosed region is same as four times area enclosed by the curve in first quadrant.