Q:Ellipse x²/16 + y²/9 = 1 Area = ?

Asked by Last Modified  

14 Answers

Learn CBSE - Class 12

Follow 2
Answer

Please enter your answer

I am a online and offline tutor with 2 years of experience on educational platform and schools.

For the ellipse x²/16 + y²/9 = 1 Here, a = 4 and b = 3. Area = πab = π × 4 × 3 = 12π square units ≈ 37.7 square units.
Comments
Dislike Bookmark

Center: $(0, 0)$ Orientation: Horizontal major axis (along the x-axis, as $16 > 9$) Semi-Major Axis ($a$): $4$ (since $a^2 = 16$) Semi-Minor Axis ($b$): $3$ (since $b^2 = 9$) Focal Distance ($c$): $\sqrt{a^2 - b^2} = \sqrt{16 - 9} = \sqrt{7} \approx 2.65$ Major Axis...
read more
Center: $(0, 0)$ Orientation: Horizontal major axis (along the x-axis, as $16 > 9$) Semi-Major Axis ($a$): $4$ (since $a^2 = 16$) Semi-Minor Axis ($b$): $3$ (since $b^2 = 9$) Focal Distance ($c$): $\sqrt{a^2 - b^2} = \sqrt{16 - 9} = \sqrt{7} \approx 2.65$ Major Axis Vertices: $(\pm 4, 0)$ Minor Axis Vertices (Co-vertices): $(0, \pm 3)$ Foci: $(\pm\sqrt{7}, 0)$ Length of Major Axis: $2a = 8$ Length of Minor Axis: $2b = 6$ Eccentricity ($e$): $\frac{c}{a} = \frac{\sqrt{7}}{4} \approx 0.661$ Directrices: $x = \pm\frac{a^2}{c} = \pm\frac{16}{\sqrt{7}}$ Length of Latus Rectum: $\frac{2b^2}{a} = \frac{2(9)}{4} = \frac{9}{2} = 4.5$ read less
Comments
Dislike Bookmark

C language Faculty (online Classes )

Find the area of the region bounded by the ellipse (x2/16) + (y2/9) = 1. A. The given ellipse (x2/16) + (y2/9)=1 can be represented as given below: Ellipse is symmetrical about x-axis and y-axis.So, area bounded by ellipse = 4 x Area of OAB Areaof OAB=∫04ydx     =∫0431−x216dx     =34∫0416−x2dx     =3404     =34−34     =34×8π2     =3π square unitsTherefore,area...
read more
Find the area of the region bounded by the ellipse (x2/16) + (y2/9) = 1. A. The given ellipse (x2/16) + (y2/9)=1 can be represented as given below: Ellipse is symmetrical about x-axis and y-axis.So, area bounded by ellipse = 4 x Area of OAB Areaof OAB=∫04ydx     =∫0431−x216dx     =34∫0416−x2dx     =34[x216−x2+162sin−1x4]04     =34[4216−42+162sin−144]−34[0216−02+162sin−104]     =34×8π2     =3π square unitsTherefore,area bounded by ellipse     =4×Areaof OAB     =4×3π square units     =12 π square units read less
Comments
Dislike Bookmark

Professional experience with 7 years of experience in Corporate industry

12π sq units
Comments
Dislike Bookmark

answer image
Comments
Dislike Bookmark

Here is the complete geometric analysis of the ellipse given by the equation: $$\frac{x^2}{16} + \frac{y^2}{9} = 1$$ 📊 Key Geometric Properties Standard Form: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ Orientation: Horizontal major axis (since $a^2 > b^2$) Semi-major axis ($a$): $4$ (since...
read more
Here is the complete geometric analysis of the ellipse given by the equation: $$\frac{x^2}{16} + \frac{y^2}{9} = 1$$ 📊 Key Geometric Properties Standard Form: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ Orientation: Horizontal major axis (since $a^2 > b^2$) Semi-major axis ($a$): $4$ (since $a^2 = 16$) Semi-minor axis ($b$): $3$ (since $b^2 = 9$) 🔍 Detailed Components Center: $(0, 0)$ Vertices (on the major axis): $(\pm 4, 0)$ Co-vertices (on the minor axis): $(0, \pm 3)$ Foci: First, find the linear eccentricity ($c$) using $c^2 = a^2 - b^2$:$$c^2 = 16 - 9 = 7 \implies c = \sqrt{7} \approx 2.65$$ Foci coordinates: $(\pm \sqrt{7}, 0)$ Eccentricity ($e$):$$e = \frac{c}{a} = \frac{\sqrt{7}}{4} \approx 0.66$$ Directrices:$$x = \pm \frac{a^2}{c} = \pm \frac{16}{\sqrt{7}}$$ Length of Major Axis: $2a = \mathbf{8}$ Length of Minor Axis: $2b = \mathbf{6}$ Length of Latus Rectum:$$\frac{2b^2}{a} = \frac{2(9)}{4} = \mathbf{4.5}$$ read less
Comments
Dislike Bookmark

Comments
Dislike Bookmark

answer image
Comments
Dislike Bookmark

Professional experience with 7 years of experience in Corporate industry

12π ≈ 37.70 sq. units
Comments
Dislike Bookmark

Maths wizard

π*4*3=12π
Comments
Dislike Bookmark

View 12 more Answers

Related Questions

In how many ways a Captain, Vice Captian and Wicket Keeper can be selected from a group of 11 cricketers.
11P3
Franziska
Do you have online classes for Math?
yes
Padma
P P Limited is Share Broker Company. G G Limited is engaged in manufacturing of packaged food. P P Limited purchased 5,000 equity shares of Rs. 100 each of Savita Limited. G G Limited also purchased 10,000 equity shares of Rs. 100 each of Savita Limited. For the purpose of preparing their respective Cash Flow Statements, under which category of activities the purchase of shares will be classified by P P Limited and G G Limited?
For GG limited it is an investment so it come in Investing Activity but as PP Ltd business is of selling shares so it will be part of Operating Activity :)
Balakrishna
There are 4 men and 3 women sitting on the round table. In how many ways can they be seated such that 1 women come in between 2 men?
168
Raja Lekshmi
I'm NEET qualified and thinking about giving Biology tution for board and medical entrance exam preparation. Tell me what you think about my decision?
Its good that you are thinking to teach, but i think its time for you to study now and built your carrer, along with studies if you have spare time you can engage classes for 1 or 2 hrs a day. In this...
Priyanka Sharma

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

The Many Ways to Combine Matrices

Saurav

1 0
View Comments0
If (x+a)(x+1991) + 1 Can Be Factored As (x+b)(x+c) Where B,C Are Integers Then Find The Sum Of All Possible Integral Values Of A?
Answer: Method 1: x^2+(1991+a)x+1991a+1 Now for integers d should be either 0 or perfect square so, (1991+a)^2-4*1991a-4 (1991-a)^2-4 (1989-a)(1993-a) They both can be equal so for d = 0 a = 1989,...

Sujoy Das

2 0
View Comments0
lecture on calculus
https://vz-3ad30922-ba4.b-cdn.net/b32e434d-e960-43da-9b86-7e192b416dc8/play_480p.mp4

Aakrsh

0 0
View Comments0
What are the Types of Credit Control Measures ? Explain it .
Types of Credit Control MeasuresA. Quantitative (General) MeasuresThese regulate the overall supply of money and credit in the economy.1. Repo RateThe rate at which RBI lends to commercial banks.Increase...

Suraj A.

0 0
View Comments0
Magnetism and Matter Overview

Sahil Kalra

0 0
View Comments0

Recommended Articles

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Meet Urmila, an MBBS tutor from Bangalore

Urmila is a passionate teacher with over 8 years of experience in teaching. She is currently pursuing her Ph. D. She provides classes for Class 11, Class 12, MBBS and Medical tuition.  Urmila began her career in teaching long before she became a teacher. She used to provide classes for foreign national students in her college...

Read full article >

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Meet Radhe Shyam Burman, an MBA Tutor from...

Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that’s where Radhe Shyam’s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...

Read full article >

Find Class 12 Tuition near you
Class 12 Tuition in Delhi
Class 12 Tuition in Bangalore
Class 12 Tuition in Hyderabad
Class 12 Tuition in Chennai
Class 12 Tuition in Kolkata
Class 12 Tuition in Mumbai
Class 12 Tuition in Pune
Class 12 Tuition in Jaipur
Class 12 Tuition in Lucknow
Class 12 Tuition in Noida
Online Tuition Class 12

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you