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If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum is
- a)39/4
- b)12
- c)15
- d)37/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the eccentricity of an ellipse be 5/8 and the distance between its ...
To find the latus rectum of the ellipse, we need to first determine the length of the major axis.
Given:
Eccentricity (e) = 5/8
Distance between foci (2ae) = 10
Let's denote the major axis as 2a and the minor axis as 2b.
Using the formula for the distance between foci:
2ae = 10
(2)(5/8)(a) = 10
(5/4)(a) = 10
a = 10 * (4/5)
a = 8
Now, let's find the value of b using the eccentricity:
e = c/a
5/8 = c/8
c = 5
So, the coordinates of the foci are (-c, 0) and (c, 0), which are (-5, 0) and (5, 0) respectively.
The equation of the ellipse in standard form is given by:
x^2/a^2 + y^2/b^2 = 1
Substituting the values of a and b, we get:
x^2/8^2 + y^2/b^2 = 1
x^2/64 + y^2/b^2 = 1
Now, let's find the length of the latus rectum:
The length of the latus rectum is given by the formula 2b^2/a.
Substituting the values of a and b, we get:
2b^2/a = 2(8^2)/8 = 16
Therefore, the length of the latus rectum is 16.
Given:
Eccentricity (e) = 5/8
Distance between foci (2ae) = 10
Let's denote the major axis as 2a and the minor axis as 2b.
Using the formula for the distance between foci:
2ae = 10
(2)(5/8)(a) = 10
(5/4)(a) = 10
a = 10 * (4/5)
a = 8
Now, let's find the value of b using the eccentricity:
e = c/a
5/8 = c/8
c = 5
So, the coordinates of the foci are (-c, 0) and (c, 0), which are (-5, 0) and (5, 0) respectively.
The equation of the ellipse in standard form is given by:
x^2/a^2 + y^2/b^2 = 1
Substituting the values of a and b, we get:
x^2/8^2 + y^2/b^2 = 1
x^2/64 + y^2/b^2 = 1
Now, let's find the length of the latus rectum:
The length of the latus rectum is given by the formula 2b^2/a.
Substituting the values of a and b, we get:
2b^2/a = 2(8^2)/8 = 16
Therefore, the length of the latus rectum is 16.
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If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum isa)39/4b)12c)15d)37/2Correct answer is option 'A'. Can you explain this answer?
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If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum isa)39/4b)12c)15d)37/2Correct answer is option 'A'. 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 eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum isa)39/4b)12c)15d)37/2Correct answer is option 'A'. 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 eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum isa)39/4b)12c)15d)37/2Correct answer is option 'A'. Can you explain this answer?.
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