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An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]
- a)4x2 + y2 = 4
- b)x2 + 4y2 = 8
- c)4x2 + y2 = 8
- d)x2 + 4y2 = 16
Correct answer is option 'D'. Can you explain this answer?
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An ellipse is drawn by taking a diameter of the circle (x – 1)2 ...
And y axes) and using each half as a radius to draw the ellipse. The equation of an ellipse is given by:
(x/a)^2 + (y/b)^2 = 1
where a and b are the lengths of the semi-major and semi-minor axes, respectively.
To find the equation of an ellipse given its center and major and minor axes lengths, you need to determine the values of a and b.
Let's say the center of the ellipse is (h, k) and the lengths of the major and minor axes are 2a and 2b. The equation of the ellipse can be written as:
((x - h)/a)^2 + ((y - k)/b)^2 = 1
where (x, y) are the coordinates of any point on the ellipse.
For example, if the center of the ellipse is (2, -3) and the lengths of the major and minor axes are 8 and 4, respectively, the equation of the ellipse becomes:
((x - 2)/4)^2 + ((y + 3)/2)^2 = 1
(x/a)^2 + (y/b)^2 = 1
where a and b are the lengths of the semi-major and semi-minor axes, respectively.
To find the equation of an ellipse given its center and major and minor axes lengths, you need to determine the values of a and b.
Let's say the center of the ellipse is (h, k) and the lengths of the major and minor axes are 2a and 2b. The equation of the ellipse can be written as:
((x - h)/a)^2 + ((y - k)/b)^2 = 1
where (x, y) are the coordinates of any point on the ellipse.
For example, if the center of the ellipse is (2, -3) and the lengths of the major and minor axes are 8 and 4, respectively, the equation of the ellipse becomes:
((x - 2)/4)^2 + ((y + 3)/2)^2 = 1
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An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer?
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An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. 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 An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer?.
An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. 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 An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer?.
Solutions for An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer?, a detailed solution for An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]a)4x2 + y2 = 4b)x2 + 4y2 = 8c)4x2 + y2 = 8d)x2 + 4y2 = 16Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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