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Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Then
  • a)
    SP = SN
  • b)
    SP = PQ
  • c)
    PN = SP
  • d)
    NQ = SP
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Q is a point on the auxiliary circle of an ellipse. P is the correspon...
P = (acosθ, bsinθ)
Q = (acosθ, asinθ)
equation of tangent at Q 
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Most Upvoted Answer
Q is a point on the auxiliary circle of an ellipse. P is the correspon...
Explanation:

  • Let us consider an ellipse with center 'O' and point 'S' as one of its foci.

  • Let Q be a point on the auxiliary circle of the ellipse and P be the corresponding point on the ellipse.

  • Thus, OQ is a minor axis of the ellipse and OP is a perpendicular from P to OQ.

  • Let SN be the perpendicular from S to the tangent of the auxiliary circle at Q.

  • As S is a focus of the ellipse, SN is a directrix of the ellipse.

  • Therefore, PN is equal to the distance between P and SN.

  • Also, as Q is on the auxiliary circle, SQ is equal to the distance between Q and SN.

  • As OQ is a minor axis of the ellipse, OQ is perpendicular to PQ.

  • Therefore, SQ is also perpendicular to PQ.

  • Thus, PN and SQ are parallel.

  • Also, as SP is a tangent to the ellipse at P, SP is perpendicular to OP.

  • Therefore, SP is also perpendicular to OQ.

  • Thus, SP and SQ are perpendicular.

  • Therefore, SPNQ is a rectangle.

  • Thus, SP and SN are equal.

  • Hence, option 'A' is the correct answer.

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Community Answer
Q is a point on the auxiliary circle of an ellipse. P is the correspon...
If You Want To Try This As Objective One Then All Points Will Coincide At Extremities of Major axis
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Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Thena)SP = SNb)SP = PQc)PN = SPd)NQ = SPCorrect answer is option 'A'. Can you explain this answer?
Question Description
Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Thena)SP = SNb)SP = PQc)PN = SPd)NQ = SPCorrect 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 Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Thena)SP = SNb)SP = PQc)PN = SPd)NQ = SPCorrect 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 Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Thena)SP = SNb)SP = PQc)PN = SPd)NQ = SPCorrect answer is option 'A'. Can you explain this answer?.
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