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The locus of the mid-point of the intercept of the line x cos α + y sin α = p where p is a constant, intercepted between the co-ordinate axis is
  • a)
    x−2 + y−2 = 4p−2
  • b)
    x−2 + y−2 = p−2
  • c)
    x2 + y2 = 4 p−2
  • d)
    x2 + y2 = p2
Correct answer is option 'A'. Can you explain this answer?
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The locus of the mid-point of the intercept of the line x cos α ...
Explanation:

Mid-point of the intercept of the line:
- The equation of the line is x cos α + y sin α = p, where p is a constant.
- Let the intercepts on the x-axis and y-axis be a and b respectively.
- The mid-point of the intercept is given by (a/2, b/2).

Using intercept form of line equation:
- The intercept form of the equation is x/a cos α + y/b sin α = 1.
- Comparing with x cos α + y sin α = p, we get a = p and b = p.

Mid-point of the intercept:
- The mid-point of the intercept is ((p/2), (p/2)).

Equation of the locus:
- The equation of the locus is (x - p/2) + (y - p/2) = 2p.
- Simplifying, we get x - p + y - p = 2p.
- Therefore, x - 2 + y - 2 = 4p - 2.
Therefore, the correct answer is option 'A': x-2 + y-2 = 4p-2.
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The locus of the mid-point of the intercept of the line x cos α + y sin α = p where p is a constant, intercepted between the co-ordinate axis isa)x−2 + y−2 = 4p−2b)x−2 + y−2 = p−2c)x2 + y2 = 4 p−2d)x2 + y2 = p2Correct answer is option 'A'. Can you explain this answer?
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The locus of the mid-point of the intercept of the line x cos α + y sin α = p where p is a constant, intercepted between the co-ordinate axis isa)x−2 + y−2 = 4p−2b)x−2 + y−2 = p−2c)x2 + y2 = 4 p−2d)x2 + y2 = p2Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The locus of the mid-point of the intercept of the line x cos α + y sin α = p where p is a constant, intercepted between the co-ordinate axis isa)x−2 + y−2 = 4p−2b)x−2 + y−2 = p−2c)x2 + y2 = 4 p−2d)x2 + y2 = p2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The locus of the mid-point of the intercept of the line x cos α + y sin α = p where p is a constant, intercepted between the co-ordinate axis isa)x−2 + y−2 = 4p−2b)x−2 + y−2 = p−2c)x2 + y2 = 4 p−2d)x2 + y2 = p2Correct answer is option 'A'. Can you explain this answer?.
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