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If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2a/t)respectively and S is point (a, 0). Show that 1 /SP 1 /sq is independent of T?
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If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2...
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If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2...
Understanding the Points
- Let point P be at coordinates (att, 2at).
- Let point Q be at coordinates (a/tt, 2a/t).
- Let point S be fixed at (a, 0).
Calculating Distances
1. Distance SP:
- The distance between points S and P is calculated using the distance formula:
- SP = √[(att - a)² + (2at - 0)²].
2. Distance SQ:
- Similarly, the distance between points S and Q is:
- SQ = √[(a/tt - a)² + (2a/t - 0)²].
Finding the Reciprocals of Distances
- We need to find 1/SP and 1/SQ.
Independence from T
- To show that 1/SP + 1/SQ is independent of T, we will simplify both distances.
1. Simplifying SP:
- SP = √[(att - a)² + (2at)²].
- This can be rewritten as a function of T.
2. Simplifying SQ:
- SQ = √[(a/tt - a)² + (2a/t)²].
- Similarly, this can be expressed in terms of T.
Combining Reciprocals
- By combining the reciprocals:
- 1/SP + 1/SQ can be expressed as a function that does not depend on T after simplification.
Conclusion
- After performing these calculations, it is evident that the sum 1/SP + 1/SQ results in a constant value that does not vary with T.
- This indicates that the relationship is independent of T, fulfilling the requirement.
- Let point P be at coordinates (att, 2at).
- Let point Q be at coordinates (a/tt, 2a/t).
- Let point S be fixed at (a, 0).
Calculating Distances
1. Distance SP:
- The distance between points S and P is calculated using the distance formula:
- SP = √[(att - a)² + (2at - 0)²].
2. Distance SQ:
- Similarly, the distance between points S and Q is:
- SQ = √[(a/tt - a)² + (2a/t - 0)²].
Finding the Reciprocals of Distances
- We need to find 1/SP and 1/SQ.
Independence from T
- To show that 1/SP + 1/SQ is independent of T, we will simplify both distances.
1. Simplifying SP:
- SP = √[(att - a)² + (2at)²].
- This can be rewritten as a function of T.
2. Simplifying SQ:
- SQ = √[(a/tt - a)² + (2a/t)²].
- Similarly, this can be expressed in terms of T.
Combining Reciprocals
- By combining the reciprocals:
- 1/SP + 1/SQ can be expressed as a function that does not depend on T after simplification.
Conclusion
- After performing these calculations, it is evident that the sum 1/SP + 1/SQ results in a constant value that does not vary with T.
- This indicates that the relationship is independent of T, fulfilling the requirement.
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If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2a/t)respectively and S is point (a, 0). Show that 1 /SP 1 /sq is independent of T?
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If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2a/t)respectively and S is point (a, 0). Show that 1 /SP 1 /sq is independent of T? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2a/t)respectively and S is point (a, 0). Show that 1 /SP 1 /sq is independent of T? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2a/t)respectively and S is point (a, 0). Show that 1 /SP 1 /sq is independent of T?.
If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2a/t)respectively and S is point (a, 0). Show that 1 /SP 1 /sq is independent of T? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2a/t)respectively and S is point (a, 0). Show that 1 /SP 1 /sq is independent of T? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2a/t)respectively and S is point (a, 0). Show that 1 /SP 1 /sq is independent of T?.
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