Question

Area bounded by the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ is equal to (a) $6 \pi$ sq units (b) $3 \pi$ sq units (c) $12 \pi$ sq units (d) area bounded by the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

Name: Problem 28, Chapter 3: Integral Calculus IIT JEE
Uploaded: 2021-07-23T19:08:37-08:00
Duration: 1 min 27 s
Channel: Vikash Ranjan
Description: Area bounded by the ellipse (x^2)/(4)+(y^2)/(9)=1 is equal to (a) 6 πsq units (b) 3 πsq units (c) 12 πsq units (d) area bounded by the ellipse (x^2)/(9)+(y^2)/(4)=1

   Area bounded by the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ is equal to
(a) $6 \pi$ sq units
(b) $3 \pi$ sq units
(c) $12 \pi$ sq units
(d) area bounded by the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

Integral Calculus IIT JEE

Amit M Agarwal 2018 Edition

Chapter 3, Problem 28

Instant Answer

Solved by Expert Vikash Ranjan

07/23/2021

Step 1

The semi-major axis is $\sqrt{9}=3$ and the semi-minor axis is $\sqrt{4}=2$. Show more…

Show all steps

Thanks for your feedback!

Area bounded by the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ is equal to (a) $6 \pi$ sq units (b) $3 \pi$ sq units (c) $12 \pi$ sq units (d) area bounded by the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

Play audio

Feedback

Vikash Ranjan and 64 other subject Calculus 2 / BC educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Ellipse

An ellipse is a closed, symmetric curve that forms a type of conic section resulting from slicing a cone with a plane. It exhibits two principal axes and is an important concept in geometry and analytical mathematics.

Standard Equation of an Ellipse

The standard form of an ellipse's equation is given as x²/(a²) + y²/(b²) = 1, where a and b represent the lengths of the semi-major and semi-minor axes respectively. This form allows for easy identification of the ellipse's dimensions and orientation.

Area of an Ellipse

The area enclosed by an ellipse is calculated using the formula Area = ?ab, which generalizes the area of a circle. This formula arises from scaling the unit circle by the factors a and b along the x and y axes, making it a fundamental result in understanding the geometric properties of ellipses.

Please give Ace some feedback