Class 10 Exam > Class 10 Questions > If P and Q are two points whose coordinates a...
Start Learning for Free
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?
Most Upvoted Answer
If P and Q are two points whose coordinates are (att, 2at) and (a/tt,2...
Community Answer
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.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup