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Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2 and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is √2, then which of the following statement(s) is (are) TRUE?
  • a)
    For the ellipse, the eccentricity is  and the length of the latus rectum is 1
  • b)
    For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2
  • c)
    The area of the region bounded by the ellipse between the lines 
  • d)
    The area of the region bounded by the ellipse between the lines 
Correct answer is option 'A,C'. Can you explain this answer?
Verified Answer
Consider two straight lines, each of which is tangent to both the circ...
(A) The required figure for the problem is given below.

The equation of the common tangent is given as,



Hence, option (A) is correct and option (B) is wrong. (C) The following figure shows the ellipse.

The area of ellipse is calculated below.

Hence, option (C) is correct and option (D) is wrong.
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Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. Can you explain this answer?
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Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. 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 Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. Can you explain this answer?.
Solutions for Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. 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 Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. Can you explain this answer?, a detailed solution for Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. Can you explain this answer? has been provided alongside types of Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Consider two straight lines, each of which is tangent to both the circle x2 +y2 = 1/2and the parabola y2 = 4x. Let these lines intersect at the point Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is√2,then which of the following statement(s) is (are) TRUE?a)For the ellipse, the eccentricity isand the length of thelatus rectum is 1b)For the ellipse, the eccentricity is 1/2and the length of thelatus rectum is 1/2c)The area of the region bounded by the ellipse between the linesd)The area of the region bounded by the ellipse between the linesCorrect answer is option 'A,C'. Can you explain this answer? tests, examples and also practice JEE tests.
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