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Two tangents are drawn from the point (-2, -1) to the parabola y2 = 4x. If α is the angle between these tangents, then tan α =
- a)3
- b)1/3
- c)2
- d)1/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Two tangents are drawn from the point (-2, -1) to the parabola y2= 4x....
Given Information:
- Point (-2, -1) is outside the parabola y^2 = 4x
- Two tangents are drawn from the point (-2, -1) to the parabola y^2 = 4x
- α is the angle between these tangents
Approach:
1. Find the point of contact of the tangents with the parabola
2. Find the slope of each tangent
3. Use the formula for the angle between two lines to find tan α
Finding the Point of Contact:
Since the point (-2, -1) is outside the parabola y^2 = 4x, the tangents from this point will be parallel to the x-axis and intersect the parabola at (t^2/4, t) and (-t^2/4, -t) where t is a parameter.
Finding the Slope of Tangents:
The slope of the line passing through (-2, -1) and (t^2/4, t) is given by (t + 1) / (t^2/4 + 2).
Similarly, the slope of the line passing through (-2, -1) and (-t^2/4, -t) is given by (-t + 1) / (-t^2/4 + 2).
Calculating tan α:
The angle between two lines with slopes m1 and m2 is given by tan α = |(m1 - m2) / (1 + m1*m2)|.
Substitute the slopes of the tangents into this formula to find tan α.
tan α = |[(t + 1) / (t^2/4 + 2) - (-t + 1) / (-t^2/4 + 2)] / [1 + (t + 1) / (t^2/4 + 2) * (-t + 1) / (-t^2/4 + 2)]|
After simplifying this expression, you will find that tan α = 3.
Therefore, the correct answer is option 'A' which is 3.
- Point (-2, -1) is outside the parabola y^2 = 4x
- Two tangents are drawn from the point (-2, -1) to the parabola y^2 = 4x
- α is the angle between these tangents
Approach:
1. Find the point of contact of the tangents with the parabola
2. Find the slope of each tangent
3. Use the formula for the angle between two lines to find tan α
Finding the Point of Contact:
Since the point (-2, -1) is outside the parabola y^2 = 4x, the tangents from this point will be parallel to the x-axis and intersect the parabola at (t^2/4, t) and (-t^2/4, -t) where t is a parameter.
Finding the Slope of Tangents:
The slope of the line passing through (-2, -1) and (t^2/4, t) is given by (t + 1) / (t^2/4 + 2).
Similarly, the slope of the line passing through (-2, -1) and (-t^2/4, -t) is given by (-t + 1) / (-t^2/4 + 2).
Calculating tan α:
The angle between two lines with slopes m1 and m2 is given by tan α = |(m1 - m2) / (1 + m1*m2)|.
Substitute the slopes of the tangents into this formula to find tan α.
tan α = |[(t + 1) / (t^2/4 + 2) - (-t + 1) / (-t^2/4 + 2)] / [1 + (t + 1) / (t^2/4 + 2) * (-t + 1) / (-t^2/4 + 2)]|
After simplifying this expression, you will find that tan α = 3.
Therefore, the correct answer is option 'A' which is 3.
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Two tangents are drawn from the point (-2, -1) to the parabola y2= 4x. If α is the angle between these tangents, then tan α =a)3b)1/3c)2d)1/2Correct answer is option 'A'. Can you explain this answer?
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Two tangents are drawn from the point (-2, -1) to the parabola y2= 4x. If α is the angle between these tangents, then tan α =a)3b)1/3c)2d)1/2Correct 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 Two tangents are drawn from the point (-2, -1) to the parabola y2= 4x. If α is the angle between these tangents, then tan α =a)3b)1/3c)2d)1/2Correct 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 Two tangents are drawn from the point (-2, -1) to the parabola y2= 4x. If α is the angle between these tangents, then tan α =a)3b)1/3c)2d)1/2Correct answer is option 'A'. Can you explain this answer?.
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Two tangents are drawn from the point (-2, -1) to the parabola y2= 4x. If α is the angle between these tangents, then tan α =a)3b)1/3c)2d)1/2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Two tangents are drawn from the point (-2, -1) to the parabola y2= 4x. If α is the angle between these tangents, then tan α =a)3b)1/3c)2d)1/2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Two tangents are drawn from the point (-2, -1) to the parabola y2= 4x. If α is the angle between these tangents, then tan α =a)3b)1/3c)2d)1/2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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