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The normal to the curve x =  a (cos θ + θ sin θ), y = a (sin θ – θ cos θ) at any point ‘θ’ is such that
  • a)
    it makes a constant angle with the x– axis
  • b)
    it passes through the origin
  • c)
    it is at a constant distance from the origin
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The normal to the curve x = a (cos θ + θ sin θ), y =...
Dividing (2) by (1), we get
∴ Slope of normal = – cot θ
∴ Equation of normal is
⇒ y sin θ – a sin2 θ + a sin θ cos θ
= – x cos θ + a cos2 θ + a θ sin θ cos θ
⇒ x cos θ + y sin θ = a
As q varies inclination is not constant.
∴ (a) is not correct.
Clearly does not pass through (0, 0).
which is constant
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The normal to the curve x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ) at any point ‘θ’ is such thata)it makes a constant angle with the x– axisb)it passes through the originc)it is at a constant distance from the origind)none of theseCorrect answer is option 'C'. Can you explain this answer?
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The normal to the curve x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ) at any point ‘θ’ is such thata)it makes a constant angle with the x– axisb)it passes through the originc)it is at a constant distance from the origind)none of theseCorrect answer is option 'C'. 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 normal to the curve x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ) at any point ‘θ’ is such thata)it makes a constant angle with the x– axisb)it passes through the originc)it is at a constant distance from the origind)none of theseCorrect answer is option 'C'. 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 normal to the curve x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ) at any point ‘θ’ is such thata)it makes a constant angle with the x– axisb)it passes through the originc)it is at a constant distance from the origind)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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