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Find the locus of a point which move such that the sum of its distances from points A(0,0,-α) and B(0,0,α) is a constant equal to 2a?
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Find the locus of a point which move such that the sum of its distance...




Explanation:




Given Information:
- Point A: (0, 0, -α)
- Point B: (0, 0, α)
- Sum of distances from A and B = 2a




Finding the Locus:




Step 1: Calculating the Distance:
- Let the point P(x, y, z) be the locus point.
- Distance from A: √(x^2 + y^2 + (z + α)^2)
- Distance from B: √(x^2 + y^2 + (z - α)^2)




Step 2: Forming the Equation:
- Given that the sum of distances is constant:
√(x^2 + y^2 + (z + α)^2) + √(x^2 + y^2 + (z - α)^2) = 2a
- Squaring both sides and simplifying will give the locus equation.




Step 3: Simplifying the Equation:
- After squaring and simplifying, the equation will represent the locus of the point P(x, y, z) that satisfies the given condition.




Conclusion:
- The locus of the point P(x, y, z) moving such that the sum of its distances from points A and B is a constant 2a can be found using the distance formula and solving the resulting equation.


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Find the locus of a point which move such that the sum of its distances from points A(0,0,-α) and B(0,0,α) is a constant equal to 2a?
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Find the locus of a point which move such that the sum of its distances from points A(0,0,-α) and B(0,0,α) is a constant equal to 2a? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Find the locus of a point which move such that the sum of its distances from points A(0,0,-α) and B(0,0,α) is a constant equal to 2a? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the locus of a point which move such that the sum of its distances from points A(0,0,-α) and B(0,0,α) is a constant equal to 2a?.
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