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A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point is
- a)a circle
- b)a parabola
- c)an ellipse
- d)a hyperbola
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A point moves in such a way that the difference of its distance from t...
Let P(h, k) be the moving point
Conjugate equation of (i)
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A point moves in such a way that the difference of its distance from t...
Understanding the Problem
The problem states that a point moves such that the difference in its distances from two fixed points (8, 0) and (-8, 0) is always 4. We need to determine the locus of this moving point.
Identifying the Points
- Let A be (8, 0) and B be (-8, 0).
- The distance from any point P(x, y) to A is given by d1 = √[(x - 8)² + y²].
- The distance from P to B is d2 = √[(x + 8)² + y²].
Condition of the Locus
- The condition is |d1 - d2| = 4.
- This means the absolute difference in distances from points A and B is constant.
Equation Formulation
- We can break this condition into two cases:
1. d1 - d2 = 4
2. d2 - d1 = 4
- Both cases can be manipulated into a standard form that represents a hyperbola.
Conic Section Identification
- The general equation of a hyperbola is defined as the set of points where the difference in distances to two foci (here, A and B) is constant.
- Since we have established that the distance difference is 4, we confirm that the locus is indeed a hyperbola.
Conclusion
Thus, the locus of the point that maintains the specified distance difference from the two fixed points is a hyperbola.
The correct answer is option 'D'.
The problem states that a point moves such that the difference in its distances from two fixed points (8, 0) and (-8, 0) is always 4. We need to determine the locus of this moving point.
Identifying the Points
- Let A be (8, 0) and B be (-8, 0).
- The distance from any point P(x, y) to A is given by d1 = √[(x - 8)² + y²].
- The distance from P to B is d2 = √[(x + 8)² + y²].
Condition of the Locus
- The condition is |d1 - d2| = 4.
- This means the absolute difference in distances from points A and B is constant.
Equation Formulation
- We can break this condition into two cases:
1. d1 - d2 = 4
2. d2 - d1 = 4
- Both cases can be manipulated into a standard form that represents a hyperbola.
Conic Section Identification
- The general equation of a hyperbola is defined as the set of points where the difference in distances to two foci (here, A and B) is constant.
- Since we have established that the distance difference is 4, we confirm that the locus is indeed a hyperbola.
Conclusion
Thus, the locus of the point that maintains the specified distance difference from the two fixed points is a hyperbola.
The correct answer is option 'D'.
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A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect 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 A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect 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 A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect answer is option 'D'. Can you explain this answer?.
A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect 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 A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect 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 A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect answer is option 'D'. Can you explain this answer?.
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A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A point moves in such a way that the difference of its distance from two points (8, 0) and (–8, 0) always remains 4.Then the locus of the point isa)a circleb)a parabolac)an ellipsed)a hyperbolaCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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