JEE Exam > JEE Questions > The ellipse x2+ 4y2= 4is inscribed in a recta...
Start Learning for Free
The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse is
- a)x2 + 12y2 = 16
- b)4x2 + 48y2 = 48
- c)4x2 + 64y2 = 48
- d)x2 + 16y2 = 16
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coo...
Let the equation of the required ellipse be 
But the ellipse passes through the point (2, 1)
Hence, equation is
But the ellipse passes through the point (2, 1)
Hence, equation is
Free Test
FREE
| Start Free Test |
Community Answer
The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coo...
To find the equation of the ellipse inscribed in a rectangle aligned with the coordinate axes, we can use the given equation of the ellipse and the fact that it is inscribed in a rectangle.
1. Understanding the given equation and ellipse:
The equation of the ellipse is x^2/4 + y^2/1 = 1. This equation represents an ellipse centered at the origin (0,0), with a major axis of length 2a = 4 and a minor axis of length 2b = 2.
2. Finding the dimensions of the rectangle:
Since the rectangle is aligned with the coordinate axes, the length of the rectangle will be 2a and the width will be 2b. Therefore, the dimensions of the rectangle are length = 4 and width = 2.
3. Finding the coordinates of the corners of the rectangle:
The corners of the rectangle can be found by using the midpoints of the major and minor axes of the ellipse. The midpoints are (±a, 0) and (0, ±b).
The coordinates of the corners are:
A = (-2, -1)
B = (-2, 1)
C = (2, 1)
D = (2, -1)
4. The rectangle inscribed in another ellipse:
We are given that the rectangle is inscribed in another ellipse that passes through the point (4, 0). This means that the coordinates (4, 0) lie on the larger ellipse.
5. Finding the equation of the larger ellipse:
To find the equation of the larger ellipse, we can substitute the coordinates (4, 0) into the equation of an ellipse.
(4^2)/a^2 + (0^2)/b^2 = 1
Simplifying, we get:
16/a^2 = 1
From this, we can determine that a^2 = 16.
6. The equation of the larger ellipse:
Using the values of a^2 and b^2 from the smaller ellipse, we can write the equation of the larger ellipse.
x^2/16 + y^2/b^2 = 1
Substituting the value of b^2 from the smaller ellipse (b^2 = 1), we get:
x^2/16 + y^2 = 1
7. Simplifying the equation:
To simplify the equation further, we can multiply both sides by 16 to eliminate the fractions.
x^2 + 16y^2 = 16
This is the equation of the larger ellipse.
8. Comparing with the given options:
The equation of the larger ellipse is x^2 + 16y^2 = 16, which matches the form of option A: x^2 - 12y^2 = 16.
Therefore, the correct answer is option A: x^2 - 12y^2 = 16.
1. Understanding the given equation and ellipse:
The equation of the ellipse is x^2/4 + y^2/1 = 1. This equation represents an ellipse centered at the origin (0,0), with a major axis of length 2a = 4 and a minor axis of length 2b = 2.
2. Finding the dimensions of the rectangle:
Since the rectangle is aligned with the coordinate axes, the length of the rectangle will be 2a and the width will be 2b. Therefore, the dimensions of the rectangle are length = 4 and width = 2.
3. Finding the coordinates of the corners of the rectangle:
The corners of the rectangle can be found by using the midpoints of the major and minor axes of the ellipse. The midpoints are (±a, 0) and (0, ±b).
The coordinates of the corners are:
A = (-2, -1)
B = (-2, 1)
C = (2, 1)
D = (2, -1)
4. The rectangle inscribed in another ellipse:
We are given that the rectangle is inscribed in another ellipse that passes through the point (4, 0). This means that the coordinates (4, 0) lie on the larger ellipse.
5. Finding the equation of the larger ellipse:
To find the equation of the larger ellipse, we can substitute the coordinates (4, 0) into the equation of an ellipse.
(4^2)/a^2 + (0^2)/b^2 = 1
Simplifying, we get:
16/a^2 = 1
From this, we can determine that a^2 = 16.
6. The equation of the larger ellipse:
Using the values of a^2 and b^2 from the smaller ellipse, we can write the equation of the larger ellipse.
x^2/16 + y^2/b^2 = 1
Substituting the value of b^2 from the smaller ellipse (b^2 = 1), we get:
x^2/16 + y^2 = 1
7. Simplifying the equation:
To simplify the equation further, we can multiply both sides by 16 to eliminate the fractions.
x^2 + 16y^2 = 16
This is the equation of the larger ellipse.
8. Comparing with the given options:
The equation of the larger ellipse is x^2 + 16y^2 = 16, which matches the form of option A: x^2 - 12y^2 = 16.
Therefore, the correct answer is option A: x^2 - 12y^2 = 16.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer?
Question Description
The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer?.
The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer?.
Solutions for The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The ellipse x2+ 4y2= 4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0). Then, the equation of the ellipse isa)x2+ 12y2 = 16b)4x2+ 48y2 = 48c)4x2+ 64y2= 48d)x2+ 16y2= 16Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup