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If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is
- a)2√3
- b)√3
- c)3/√2
- d)3√2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If the distance between the foci of an ellipse is 6 and the distance b...
Given,
2ae = 6 .... (1)
∴ ae = 3
Also,
2a/e = 126 .... (2)
∴ a/e = 63
From (1) and (2),
Since b2 = a2(1 - e2)
Substitute the values of 'e' and 'a' in the above equation.
⇒ b2 = 9
∴ b = ±3
Length of latus rectum
2ae = 6 .... (1)
∴ ae = 3
Also,
2a/e = 126 .... (2)
∴ a/e = 63
From (1) and (2),
Since b2 = a2(1 - e2)
Substitute the values of 'e' and 'a' in the above equation.
⇒ b2 = 9
∴ b = ±3
Length of latus rectum
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Community Answer
If the distance between the foci of an ellipse is 6 and the distance b...
The length of the latus rectum of an ellipse is given by the equation:
latus rectum = 2b^2/a
where a is the distance between the center of the ellipse and one of its vertices, and b is the distance between the center of the ellipse and one of its co-vertices.
In this case, the distance between the foci of the ellipse is 6, so a = 6/2 = 3.
The distance between the directrices of the ellipse is 12, so b = 12/2 = 6.
Substituting these values into the equation for the length of the latus rectum, we get:
latus rectum = 2(6^2)/3 = 2(36)/3 = 2(12) = 24
Therefore, the length of the latus rectum of the ellipse is 24.
latus rectum = 2b^2/a
where a is the distance between the center of the ellipse and one of its vertices, and b is the distance between the center of the ellipse and one of its co-vertices.
In this case, the distance between the foci of the ellipse is 6, so a = 6/2 = 3.
The distance between the directrices of the ellipse is 12, so b = 12/2 = 6.
Substituting these values into the equation for the length of the latus rectum, we get:
latus rectum = 2(6^2)/3 = 2(36)/3 = 2(12) = 24
Therefore, the length of the latus rectum of the ellipse is 24.
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If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum isa)2√3b)√3c)3/√2d)3√2Correct answer is option 'D'. Can you explain this answer?
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If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum isa)2√3b)√3c)3/√2d)3√2Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum isa)2√3b)√3c)3/√2d)3√2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum isa)2√3b)√3c)3/√2d)3√2Correct answer is option 'D'. Can you explain this answer?.
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